Activate yeast: In a small bowl, combine warm milk, 1 tbsp sugar, and yeast. Let sit 5 minutes until foamy.
Make dough: In a large bowl or mixer, combine flour, remaining sugar, and salt. Add yeast mixture, softened butter, and egg. Knead until dough is smooth and elastic (about 8-10 minutes).
First rise: Place dough in a greased bowl, cover, and let rise in a warm spot for about 1 hour, or until doubled.
Prepare cheesecake filling: Beat cream cheese, powdered sugar, and vanilla until smooth. Set aside.
Make strawberry compote: In a saucepan, combine strawberries, sugar, and lemon juice. Simmer on medium heat until thickened (about 10 minutes). Cool completely.
Assemble rolls: Roll dough into a rectangle (about 12x16 inches). Spread cheesecake filling evenly, then top with strawberry compote.
Roll & slice: Roll dough tightly from the long side, chill 15 minutes for easier slicing. Cut into 12 equal rolls.
Second rise: Place rolls in a greased or parchment-lined 9x13 pan, cover, and let rise 30 minutes until puffy.
Bake: Preheat oven to 350°F (175°C). Bake rolls 25–30 minutes until golden brown.
Glaze: Mix powdered sugar and milk until smooth. Drizzle over warm rolls. Cool slightly before serving.