Preheat oven to 450 degrees F (230 degrees C). Grease a baking sheet.
To make biscuits, mix the self-rising flour and sugar together in a bowl, and stir in the melted butter and 3/4 cup of milk. Knead the dough very lightly for 5 to 7 times, until it barely hangs together, and roll out to 1/2 inch thick on a floured surface.
Cut biscuits with a biscuit cutter or the rim of a glass dipped in flour.
Bake in the preheated oven for 12 to 14 minutes, until the biscuits are golden brown.
Melt 2 tablespoons of butter in a large skillet over medium heat, and place the deer meat into the hot butter.
Sprinkle the meat with salt and pepper, and pan-fry until golden brown, about 5 minutes.
Remove the meat to a platter.
Pour the chicken broth into the skillet, and bring to a boil while scraping the browned bits off of the bottom of the skillet with a wooden spoon. Stir in 1 cup of milk and the maple syrup, and whisk in all-purpose flour until smooth. Bring the gravy back to a simmer, add salt and pepper to taste, and allow to thicken, whisking to avoid lumps. Return the deer meat to the gravy, and simmer until the gravy is thick, 5-10 minutes.
