For the empanadas: Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
Add olive oil to lightly coat a medium saute pan over medium heat. Add the red onion and cook until just translucent, about 5 minutes. Add the garlic and jalapeno and cook for an additional 3 minutes. Add the corn, cilantro and crab and stir to combine. Taste and season with salt and crushed red pepper. Remove from the heat and allow to cool slightly until cool enough to handle.
Meanwhile, roll out each dough into 11-inch rounds, using flour as needed to avoid sticking. Cut the dough using a cookie cutter or lip of a glass into desired size, anywhere from 4 to 6 inches. Use all of the dough, putting scraps together and rolling out again. Divide filling equally among all of the dough, placing the filling in the center. Brush the sides of the dough lightly with the egg wash and fold to form a half moon. Press the edges together with a fork to seal. Place on the baking sheet about 2 inches apart and brush with the remaining egg wash. Using a fork, poke a few holes in the top of each empanada to allow steam to escape while baking. Bake until the dough is golden brown and flaky, about 20 minutes. Remove from the oven and serve with the aioli.
For the aioli: Add the garlic, vinegar, lime zest and juice and egg yolks to the bowl of a food processor. Turn the machine on. While the machine is running, begin adding the oil, drop by drop, until you see the mixture thicken. When the mixture begins to look like a smooth homogeneous mixture, the oil can be added in a slow thin stream. If the mixture is too thick, add a few drops of water to thin it down. Season with salt and taste to make sure it is delicious.