Combine warm milk, yeast, and 1 tablespoon of sugar in a bowl; let stand for 5 minutes until blooming occurs.
Whisk in the remaining sugar, melted butter, egg, and salt. Gradually incorporate flour until a cohesive dough forms.
Knead the dough by hand or mixer for 7 minutes until smooth. Place in a greased bowl, cover, and proof in a warm environment for 90 minutes.
While dough rises, simmer diced peaches, brown sugar, 1 teaspoon cinnamon, nutmeg, and cornstarch in a saucepan over medium heat for 5 minutes until thickened. Cool completely.
Punch down the dough and roll into a 12x18 inch rectangle on a floured surface.
Spread softened butter over the dough, followed by the remaining cinnamon and the cooled peach compote.
Roll the dough tightly from the long edge and slice into 12 equal portions using a serrated knife or dental floss.
Arrange rolls in a greased 9x13 inch baking pan. Cover and proof for 30 minutes.
Preheat oven to 350°F. Combine cold cubed butter, 1/4 cup flour, and 1/4 cup sugar to create a crumbly streusel; sprinkle over the rolls.
Bake for 25 minutes until the internal temperature reaches 190°F and the tops are golden brown.
Whisk powdered sugar, heavy cream, and vanilla to create a glaze. Drizzle over the rolls while still warm.