Add the butter and peaches to a pan over medium-low heat and cook until the butter has melted and peaches are glossy. Leave heat on and pan on stove.
In a separate small bowl mix together the brown sugar, cinnamon, 1 tablespoon flour, and nutmeg. Sprinkle the sugar mixture over the peaches. Mix to combine and stir for 5-10 minutes until the mixture starts to thicken. Remove from heat and set aside to cool.
Sprinkle some extra flour on a countertop or the surface you're working on, roll out the pizza dough to ¼-inch thick. Cut the dough into same-sized 20 rectangles.
Spoon 1 tablespoon of the peach filling onto a cut piece of dough. Fold the dough over lengthwise and crimp the edges (pinchth em tight) so the filling is well sealed. Repeat with remaining dough and filling.
Heat oil in a large pot to 350°F
Working in batches, fry beignets for 3-4 minutes each, flipping halfway, until puffy and golden brown.
Transfer beignets to a paper towel-lined plate, and continue until they are all done.
Dust with as much powdered sugar as you like, and dig in!