Position a rack in the center of the oven and preheat to 425°F (218°C). Line 14 muffin cups with liners or spray generously with nonstick spray. Set aside.
In a small bowl, whisk the brown sugar, flour, and cinnamon. Cut in the cold butter using a pastry knife or mix with a fork until the mixture resembles coarse crumbs. Don't overwork it—leaving some pea-sized pieces of butter creates the best crunchy clusters. Set aside in the fridge.
In a medium bowl using a handheld or stand mixer fitted with a paddle attachment, beat the softened butter on high speed until smooth and creamy, about 1 minute. Add the granulated and brown sugars and beat on high until creamed, about 2 full minutes. Scrape down the sides and bottom of the bowl. The mixture should look light and fluffy.
Add the eggs, yogurt, and vanilla extract. Beat on medium speed for 1 minute, then turn up to high speed until the mixture is combined and uniform in texture. Scrape down the sides and bottom of the bowl. Don't worry if it looks slightly curdled at this point—it will come together when you add the flour.
In a large bowl, whisk together the flour, baking soda, baking powder, and salt. Pour the wet ingredients into the dry ingredients and slowly mix until combined and little lumps remain. Overmixing is the enemy of the tender muffin, so stop as soon as you don't see dry flour.
Using a wooden spoon or rubber spatula, gently fold in the strawberries. Don't worry if the berries bleed a little—I actually love how the batter turns a pretty pink in spots; it looks gorgeous when baked.
In a medium bowl, beat the softened cream cheese with an electric handheld or stand mixer on medium-high speed until creamy. Add the egg yolk, vanilla extract, and sugar. Beat until completely smooth and combined.
Spoon 1 tablespoon of strawberry muffin batter into the bottom of each prepared muffin cup. Layer with about 1 spoonful (not quite a full tablespoon) of the cheesecake filling, then another tablespoon of muffin batter (or however much batter is needed to fill the cups all the way to the top). Yes, fill the muffin cups to the very top if you want that bakery look. Some cheesecake filling may poke through on the sides or top—that's a happy accident.
Sprinkle each muffin evenly with the streusel topping and gently press the streusel down into the batter so it sticks during baking.
Bake the muffins for 5 minutes at 425°F (218°C). Then, keeping the muffins in the oven, lower the temperature down to 350°F (177°C) and bake for an additional 18 minutes, or until a toothpick inserted in the center of a muffin (aim for the muffin part, not straight into the cheesecake filling) comes out clean. The total time in the oven is about 23-24 minutes.
Allow the muffins to cool for 15 minutes in the muffin pan. The cheesecake filling needs this time to set up properly, so don't rush it. Then transfer to a wire rack to cool completely, or enjoy them warm. They are incredibly moist from the cheesecake filling.