Make the cream cheese filling. Beat cream cheese until completely smooth, about 30–45 seconds. Beat in sugar, egg yolk, and vanilla just until creamy. Set aside.

Make the streusel. Stir flour, brown sugar, cinnamon, and salt together. Add melted butter and toss gently with a fork until irregular crumbs form. Stop once you have a mixture of fine crumbs and small clumps.

Make the pumpkin batter. Whisk flour, baking soda, baking powder, salt, cinnamon, and pumpkin pie spice in a large bowl. In a separate bowl, whisk pumpkin, both sugars, eggs, oil, milk, and vanilla until smooth. Fold the dry ingredients into the wet ingredients just until the flour disappears. A few small lumps are fine; don't overmix.

Fill the muffins. Add about 1½ tablespoons batter to each liner. Spoon 1 generous tablespoon cream cheese filling into the center, keeping it away from the edges. Divide remaining batter over the filling until the cups are about ¾–⅞ full.

Add the streusel. Sprinkle generously over each muffin, lightly pressing a few larger crumbs into the batter without flattening the tops.

Bake. Bake at 425°F for 5 minutes. Without opening the oven door, reduce the temperature to 350°F and bake another 15–18 minutes. Test the pumpkin portion slightly off-center with a toothpick; it should have a few moist crumbs but no wet batter.

Cool. Leave muffins in the pan for 10 minutes, then transfer to a wire rack for another 10–15 minutes before serving. The cream cheese center sets as the muffins cool.