Activate yeast by combining warm water and milk (105-115°F), then sprinkle yeast and a pinch of sugar over the top. Let stand for 5-10 minutes until foamy.
In stand mixer bowl, combine flour, remaining sugar, and salt. Add activated yeast mixture, butter, and eggs. Mix on low for 2 minutes, then knead on medium for 8-10 minutes until smooth and elastic.
Shape dough into a ball and place in a greased bowl, turning to coat. Cover and let rise in a warm place for 1-1.5 hours until doubled in size.
While dough rises, peel and dice peaches into 1/4-inch pieces. If using canned or frozen, drain and pat dry thoroughly. Combine brown sugar, cinnamon, and nutmeg in a small bowl.
Punch down dough and roll into an 18x12 inch rectangle on a lightly floured surface. Spread softened butter over the surface, leaving a 1/2 inch border on the far long edge.
Sprinkle the brown sugar mixture evenly over the butter and press in gently. Scatter diced peaches evenly over the top.
Roll the dough tightly into a log starting from the long edge closest to you. Pinch the seam to seal. Cut the log into 12 equal pieces, about 1.5 inches thick, using a sharp knife or dental floss.
Place rolls cut-side up in a greased 9x13 inch baking dish. Cover and let rise in a warm place for 45-60 minutes until puffed and touching.
Preheat oven to 350°F (175°C). Bake for 25-30 minutes until tops are golden brown and center rolls reach 190°F. Tent with foil if browning too quickly.
Beat softened cream cheese until smooth. Mix in sifted powdered sugar, vanilla, and 3 tablespoons of milk until smooth and pourable. Add more milk if needed for desired consistency.
Cool rolls for 5-10 minutes, then generously pour or spread the glaze over the warm rolls. Serve immediately.