Preheat the oven to 425 degrees Fahrenheit. Line a 12 cup muffin tin with muffin liners (or cupcake liners).
In a small bowl, mix the 4 ounces softened cream cheese, ¼ cup white sugar and ½ beaten egg to make the cream cheese filling. You can use an electric mixer on medium speed rather than a whisk for the smoothest outcome. Once smooth, fold in the ⅓ cup chopped strawberries using a spatula.
In a large bowl, mix the all-purpose flour, baking powder and 1 cup white sugar.
In a medium bowl, combine the melted butter, olive oil, buttermilk, 2 eggs and vanilla extract. Pour the wet ingredients into the flour mixture. Whisk together until just combined, being careful not to overmix. Add the 2 cups chopped strawberries to the muffin batter and fold in with a spatula.
Fill each lined muffin cups ⅔ high with muffin batter. Add about a tablespoon of the cream cheese mixture on top and push down slightly with a spoon so it falls inside the muffin batter.
Bake in the preheated oven for 5 minutes. Turn the heat down to 350 degrees Fahrenheit and bake another 15-20 minutes, until a toothpick inserted into the center of the muffin comes out clean and the top of the muffins are golden brown.
Remove muffins from the oven and transfer to a wire rack. Let cool at room temperature for about 10 minutes before serving.