Prep the pan and oven: Line a 12-cup muffin tin with liners. Preheat oven to 425°F (220°C).
Mix dry ingredients: In a large bowl, whisk 2 cups flour, 3/4 cup sugar, 2 1/2 tsp baking powder, and 1/2 tsp salt.
Make the wet mixture: In a separate bowl, whisk 2 eggs, 1 cup milk, 1/2 cup sour cream, 1/2 cup melted butter, and 2 tsp vanilla until smooth.
Combine gently: Pour wet into dry and fold with a spatula just until a few streaks remain.
Do not overmix.
Prep strawberries: Toss 1 1/2 cups diced strawberries with 1 tbsp flour. Fold into the batter with a few gentle strokes.
Make the cream cheese filling: Beat 8 oz softened cream cheese with 1/4 cup powdered sugar and 1/2 tsp vanilla until smooth.
Fill the cups: Add about 2 tbsp batter to each liner, dollop 1 tbsp cream cheese filling in the center, then cover with more batter until cups are about 3/4 full. Sprinkle tops with coarse sugar if using.
Bake high then low: Bake at 425°F for 5 minutes.
Without opening the oven, reduce heat to 350°F (175°C) and bake 13–16 more minutes, until tops are golden and a tester in the muffin (avoid the cream cheese pocket) comes out clean.
Cool: Let muffins rest in the pan 5 minutes, then transfer to a wire rack. Cool until warm before serving so the filling sets.