In a mixing bowl or an electric mixer with a dough hook attachment, add warm water and yeast and let sit for a minute.
Add the sugar, salt, melted butter, egg and egg yolk and mix.
Add the flour a cup at a time and add until a dough forms, you may use more or less than 4 cups.
Knead dough for 5 minutes or until it feels smooth and almost gum like.
Place in a greased bowl, cover with plastic wrap or a towel and let rise for 1 hour.
While dough is rising, sauté jalapenos in a pan for 5 minutes or until they soften slightly then set aside.
Gently punch down the dough and roll it out into a large rectangle, roughly 12 inches wide by 10 inches high, it doesn't need to be exact.
Add the diced jalapenos over the top of the dough, followed by the shredded cheddar cheese.
Roll the dough up into a roll, like you would a cinnamon roll.
Once rolled, slice the dough down the middle of the roll so you have 2 pieces of the roll with the layers exposed.
Now twist the two pieces of dough together to form a twist and place in a greased baking sheet. It is okay if cheese and jalapenos fall out during the rolling, just place anything that falls out on to top of the bread.
Lightly cover the babka with greased plastic wrap and allow to rise for about 30 minutes in a warm location.
While it is rising, mix together the egg wash ingredients and before baking the babka, brush the top with egg wash.
Preheat oven to 350 F. and bake babka for 40 - 45 minutes or until center is baked, internal temperature should be between 190 - 200 F..
You can cover the top of the loaf if it is getting too brown.
Allow to mostly cool then enjoy.