Trying to figure out the best way to resolve this issue on some of my exterior windows. Is that mold? Can I just clean it and if so, with what? Or should I scrape out the old caulking, clean, re-caulk, and re-paint?

I'll bet the money in my pocket there isn't much foam left in that foam trim build out

Sorry I don't quite understand what you're saying.

Usually, that stucco trim around the window is made with rigid foam with a stucco parge coat. Many times, the foam disintegrates and the stucco facade easily fails.

In this case, if there is a foam backer, it might be holding water, or conversely, not have a proper slope to let water drain. Which direction is this window facing?

You'd need to scrape the caulk and reapply. However, there is probably a deeper cause to the discoloration.

Most of them are on the rear of the house which faces East. One window on the front has the same issue and faces West. Recommendations on how to fix long term?

Mold is a symptom of a bigger problem. Cleaning the mold off doesn't treat what caused the mold to grow in the first place.

Those sills are somehow holding onto water and creating the environment for mold to grow. It could be because the sill doesn't have a proper slope to drain water away, the stucco is absorbing water and no place for it to go, or the whole piece of stucco trim is letting water in at the bottom of the window.

AgthatBuilds is saying there's probably water damage behind that stucco bump out beneath the window. It looks like the areas that have mold are pulled away from the house and have created a path for water to get behind them.

Is this something that would be covered by the 10 year bonded builders warranty? We bought the home new in 2013. If not, how would I go about fixing long term?

Is there any interior water damage or marks? It looks like a lot of that is happening below the weep holes

No interior damage from what I can tell.

It appears to me that the problem is occuring from water that the window is shedding through its built in weeps.

Water is coming out of the weeps and stopping at the caulk and/or the stucco/foam block. If you look closely to the pics, you can see the water staining traveling up the jambs which tells me the water is sitting on the window jamb or getting under the stucco and not draining properly. It also appears the caulking has cracked and allows water to get behind the paint.

I think you should try to scrape the caulk and reapply with some NP1. I do think it's going to be very fragile and the stucco is likely to peel off with the old caulk. If the foam has disintegrated you wont have any backing to caulk to and youll probably need to call someone to fix it. If it is a wood build out, I'd bet there is some rot occurring.

The reality is that window detail is tough to properly waterproof and the water that is shed by weep holes now must travel down the top of the stucco detail and, without a proper slope, it hard for the water to drain the way you want.

Thanks. Know of anyone in the Austin area that could properly correct the issue? I'd prefer to fix it right the first time.

Im in austin but i dont have a good contact for something like that. Anyone i would send you would blow your mind regarding costs*. Maybe try abc home services?

*not because i think its an expensive repair but because my guys are super busy and their costs reflect it. It's getting quite absurd, really.

Is the window sill flat? I thought there were supposed to be angled down.

I bet if you drilled a small hole at the bottom of that stucco trim, water would start pouring out immediately. I doubt the builder warranty would do any good at this point, they will put it back on you saying that replacing caulking falls under homeowner maintenance.
I would be looking at bringing in a stucco contractor to dig into one of the windows and see what's happening behind the wall before any major damage occurs.