Beat softened cream cheese with 1/3 cup sugar until smooth. Add 1 egg and vanilla extract, mixing until fully combined. Set aside.
Cream butter and sugar for 4–5 minutes until fluffy. Add eggs one at a time, beating well after each. In another bowl, whisk flour, baking powder, and salt.
Gradually add the dry mix to the creamed mixture, alternating with sour cream. Stir in vanilla and almond extracts. Fold in diced, patted-dry strawberries.
Grease and flour a bundt or loaf pan. Pour in half the cake batter. Spread the cheesecake filling on top. Add the remaining batter and gently swirl with a butter knife.
Preheat oven to 325°F (165°C). Bake for 75–85 minutes, or until a toothpick inserted into the cake (not the filling) comes out clean.
Cover with foil if browning too fast. Cool in the pan for 20 minutes, then transfer to a wire rack.
Mix powdered sugar with 1–2 tablespoons pureed strawberries until smooth. Drizzle over the cooled cake before serving.