Heat the milk on the stove until it steams (1 or 2 wisps). Meanwhile, place yeast, sugar, and warm water in a small bowl. Stir and set aside until the mixture is frothy.
Pour the yeast mixture, milk, salt, oil, and flour in the bowl of a stand mixer.
Use the paddle attachment to mix until combined and shaggy. Remove the paddle and replace it with the dough hook. Continue to mix with the dough hook for 1-2 minutes on low speed and increase to medium speed for 5-6 additional minutes.
The dough should be smooth and elastic. Remove it from the mixer and place it in a clean bowl. Cover with a towel and allow to rest and double in size. In meantime, prepare the egg wash.
After the dough doubles, turn it out onto a well-floured surface and separate it into three equal sections. Use a rolling pin to roll one section into a 6-inch long, 8-inch wide rectangle.
Place 1/3 of the cheese and jalapenos onto the dough rectangle leaving an inch of dough exposed along the top. Use a pastry brush to apply the egg wash along the top edge.
Carefully roll the rectangle away from you, as if you were making cinnamon rolls. The egg wash will seal the tube shut. Gently press or pinch the dough along the edge to ensure sealing.
Roll the dough between your hands and the counter until it lengthens to 10-12 inches. Repeat the process with the other pieces.
Place the rolled dough onto a baking sheet lined with a silicone mat or parchment paper. Use a sharp knife to cut slits down the length of each tube taking care to only cut halfway through.
Beginning in halfway up the tubes, start to braid the dough to the end and tuck under any loose ends. Turn the baking sheet around and braid the other side and tuck under any loose ends.
Cover the braided dough with a clean kitchen towel and allow the dough to rise again. While the dough rises, preheat the oven to 400 degrees.
After the dough has doubled in size, use a pastry brush to apply the remaining egg wash to the dough. Place the baking sheet in the oven and bake for 20-25 minutes.
The bread is done when the top is golden brown and the center is no longer doughy.
Remove from the oven and allow to cool completely before serving.