Preheat and prep. Preheat your oven to 425°F (220°C). Line a muffin pan with paper liners or grease it well.
Make the crumble. In a small bowl, mix the flour, sugar, and melted butter together with a fork until crumbly. Set aside.
Make the cheesecake filling. In another small bowl, mix the softened cream cheese and icing sugar until smooth and creamy. Set aside.
Whisk the wet ingredients. In a large bowl, whisk together the sugar, melted butter, oil, yogurt, milk, vanilla, and eggs until smooth and well combined.
Add the dry ingredients. Sift the flour, baking powder, and salt directly into the wet mixture. Stir gently until just combined and no dry streaks remain. Don't overmix at this point.
Fold in the strawberries. Toss the diced strawberries in a little flour, then gently fold them into the batter.
Assemble. Divide the batter evenly between 12 muffin cups. Spoon 2 to 3 teaspoons of cheesecake filling onto the center of each. Generously sprinkle the crumble over the top of every muffin.
Bake in two stages. Bake at 425°F (220°C) for 5 minutes, then without opening the oven door, lower the temperature to 350°F (180°C) and continue baking for 15 to 18 minutes, until the tops are golden and a toothpick inserted into the muffin part comes out clean. About 20-23 min in total.
Drizzle and enjoy. Let the muffins cool slightly, then drizzle with the icing.