Combine the water and sugar in a large bowl. Sprinkle yeast on top. Allow 2-3 minutes for yeast to react with warm water and froth on top. If it does not react, then toss the yeast and start with new, fresh yeast.
Add the flour, salt, olive oil, roasted garlic, Hatch chiles and cheese and mix by hand or with your mixer dough hook just until combined.
Cover the bowl with a light layer of plastic wrap and allow to sit in a warm, draft-free place for 2-3 hours or until doubled in size. Dough will be bubbly on top with some holes, and wobbly when shaken slightly.
Place a large Dutch oven or heavy pot in the oven with an oven-safe lid. Preheat oven to 450 degrees F, 25-30 minutes before baking.
Flour a flat surface with 2 Tbsp flour and dump the dough onto the surface. Sprinkle flour on top of the surface of the dough. Fold the dough over on itself like a letter. Then flip it over and form a rough, round shape.
Measure some parchment paper for the pot that's in the oven. Put the paper, smooth side up, next to the dough you just formed. Carefully lift the dough ball, after forming, onto the middle of the parchment.
Moving quickly, remove the Dutch oven from the oven with oven mitts. Remove the lid. Use both hands to lift the parchment paper from each side and set the parchment (with the dough on it) in the pot.
Using oven mitts, place the lid on the Dutch oven and place the pot in the oven. Bake for 30 minutes at 450 degrees F.
Using oven mitts, remove the lid and bake for 15-20 minutes, or until loaf has lightly browned.
Using oven mitts, remove the pot from the oven and allow to cool before removing the bread and slicing to enjoy.