The Tex-Mex chain continues to carry the franchise for restaurant operator Yum! Brands.

Resilience, thy name is Yum! Brands (NYSE:YUM). Despite the lasting impact of its Chinese supplier scandal, the restaurant operator remains steadfastly resolute that this is a temporary situation that's working itself out. As a result, investors have mainly stuck by the owner of Taco Bell, KFC, and Pizza Hut.

Its latest earnings report showed that Yum! Brands is still on the path toward improvement, and soon enough the mess created by its second food-quality crisis in as many years will have passed. It's not all smooth sailing, though, and these are five items Yum! Brands' management thinks investors ought to keep in mind.

1. It's still steady as she goes
If you saw Yum! Brands' first-quarter earnings report, you basically saw all you needed to know for the second quarter: China's recovery is continuing apace; Taco Bell is eating up the breakfast daypart; KFC outside China is putting in a workmanlike effort; and Pizza Hut has a long, long way to go before it's out of the woods.

As CEO Gary Creed noted, "I would summarize our second-quarter performance as very similar to our first-quarter results." Essentially it's been wash, rinse, repeat.

For the most part, that is. China's still in recovery mode, but let's take a closer look at what that really means.

2. China is still the elephant in the room
Same-store sales in China improved sequentially, with comps down 10% in the second quarter compared with 12% in Q1 and 15% a year ago. However, that was a lot worse than what everyone was expecting. And because China is still the straw that stirs Yum! Brands' drink, accounting for more than half of total revenue and a third of its operating profit, that plodding turnaround is a much bigger issue than it might otherwise seem.

As Creed pointed out, Yum! Brands does have two of the strongest brands in China, "but frankly, the recovery is taking longer than we would like. We need to be more aggressive, more innovative and much more disruptive to step change the business."

3. Everybody wants Taco Bell
At least for breakfast, Taco Bell seems pretty popular. Launched in early 2014, the Taco Bell breakfast menu is a huge hit. According to Bloomberg, the daypart now accounts for about 6% of Taco Bell's overall sales, and this quarter the Mexican food chain's system sales rose by 9% on the strength of a 6% increase in comps and 3% unit growth.

However, the rapid rise to popularity of the a.m. Crunchwrap and Taco Waffle also means that investors may be disappointed going forward as Taco Bell now faces tough comparisons. Having gone a full year with breakfast, CFO Pat Grismer cautions that "although we expect solid performance in the balance of the year, we expect much more moderate profit growth as we overlap stronger sales and margin performance from last year."

Outside of China, Colonel Sanders is doing his part at KFC to keep the chicken chain afloat for Yum! Brands.

4. KFC remains A-OK
KFC was able to post some solid numbers, including same-store sales growth of 3%. In the U.S., same-store sales growth has remained positive for four straight quarters now. KFC also opened 122 new restaurants in 39 countries, almost three-quarters of which were in emerging markets. And having now gotten past the Chinese supplier crisis, management is looking for substantial growth to kick in again.

CEO Creed says that no matter where you look, "what you will see in those markets is we have great entry price points, we have great value for money, we have really chicken-focused innovation, and we are really doing disruptive things in the marketplace."

5. Pizza Hut is flatter than one of its pies
Pizza chain Pizza Hut, however, remains a great big disappointment, even if management didn't quite put it in those terms. Its turnaround is taking longer than expected, and though there are green shoots of improvement here and there -- comps came in flat for the quarter, for instance, but actually improved across the quarter -- there's no quick fix here.

Maintaining that stiff upper lip in the face of adversity, Creed said, "I firmly believe Pizza Hut has enormous potential that recent results do not reflect."

What it all means for investors
The Chinese food scandal hurt -- again -- and will continue to weigh on performance. However, there are enough moving parts in Yum!'s results that even if the company doesn't overcome the hurdles, it minimizes the sharpest points.

Taco Bell's strong sales don't supersede China's tumble. But having redefined a whole segment of its operations with a new breakfast menu means that once China does return to growth, Yum! Brands will be stronger because of it.