Preheat the oven to 425 and prepare a jumbo muffin tin with muffin liners and set to the side.
Make the cheesecake filling. Using a hand mixer in the bowl of a stand mixer with a paddle attachment, cream the cream cheese, egg yolk, vanilla, and sugar until smooth. Set to the side.
Make the muffins. In a medium-sized bowl, combine the flour, baking soda, baking powder, and salt. Set to the side.
In a large bowl, whisk the melted butter, oil, sugar, and eggs and stir until combined. Then add in the buttermilk and vanilla.
Fold in the dry ingredients to the wet ingredients using a rubber spatula. When the mixtures are combined, add in the chopped strawberries. Continue using the rubber spatula to fold the strawberries into the batter.
Pour the strawberry muffin batter into the prepared pan, layering it with the cheesecake filling. Fill the muffin tin to the top with the batter and the filling. Generously top each muffin with the coarse sugar.
Bake muffins at 425°F for 5 minutes and turn the heat down on the oven to 350°F while the muffins are in the oven. Continue to bake for 25-30 minutes, until the muffins are fully browned on top and a toothpick can run clean through them.
Let muffins slightly cool, for about 10 minutes in the pan before taking them out. Serve fresh and enjoy!
