In a medium saucepan, combine 2 cups of halved strawberries, 1/4 cup of granulated sugar, and 2 tablespoons of lemon juice. Over medium heat, simmer the mixture for 10-12 minutes, stirring occasionally until it becomes glossy and syrupy. Remove from heat and allow to cool completely.

In a mixing bowl, beat 6 ounces of softened cream cheese, 1/3 cup of powdered sugar, and 1 teaspoon of vanilla extract together until the mixture is smooth and creamy. Cover and chill in the refrigerator for about 10 minutes.

In a large bowl, whisk together 6 tablespoons of melted unsalted butter, 1/4 cup of vegetable oil, 2 large room-temperature eggs, 3/4 cup of sour cream, 1 teaspoon of vanilla extract, and 1 cup of milk until fully combined. In a separate bowl, mix 2 1/2 cups of all-purpose flour, 2 teaspoons of baking powder, 1/2 teaspoon of baking soda, 1/4 teaspoon of salt, and 1/4 cup of granulated sugar. Gently fold the wet mixture into the dry ingredients until just combined.

Gently incorporate 1 cup of chopped strawberries that have been tossed in 1/2 teaspoon of flour into the muffin batter for even distribution.

Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners. Fill each muffin liner about two-thirds full with the muffin batter and top with a dollop of cream cheese filling. Cover with more muffin batter and add a teaspoon of cooled strawberry reduction on top.

Bake for 20-25 minutes, or until golden brown and springy to the touch. Cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.