Line a small sheet pan with parchment paper. Beat the cream cheese, 3 tablespoons granulated sugar, 1 teaspoon vanilla, and the egg yolk together with a hand mixer until smooth. Drop 12 rounded tablespoon-sized scoops onto the parchment. Place the pan in the freezer for 20 minutes. This step is not optional. Firm, nearly frozen filling is the key to keeping the cream cheese centered during baking instead of oozing sideways.

While the filling chills, make the streusel. Combine the oats, 1/3 cup flour, 1/4 cup brown sugar, and 1/2 teaspoon cinnamon in a small bowl. Add the cold butter cubes and work them in with your fingertips, pressing and rubbing until the mixture clumps together like coarse, damp sand. Some larger pea-sized clumps are good. Refrigerate the streusel until needed.

Heat your oven to 375 degrees F. Line a 12-cup muffin tin with paper liners or grease the cups thoroughly.

Make the batter. Whisk the flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon together in a large bowl. In a second bowl, whisk the pumpkin puree, eggs, 3/4 cup brown sugar, oil, milk, and vanilla until smooth. Pour the wet mixture into the dry and fold with a spatula just until no flour streaks remain.

Fill each muffin cup about halfway with batter, roughly 2 tablespoons. Take a cream cheese portion from the freezer and press it gently into the center of the batter in each cup. It should sit just below flush with the batter, not on top. Cover each cup with another tablespoon or so of batter to seal the filling inside. The cups will be about 3/4 full.

Pinch and scatter the chilled streusel evenly over each muffin. Press it down very lightly so it sticks and does not slide off.

Bake on the center rack for 22 to 25 minutes. Check at the 15-minute mark. If the streusel is turning deep brown before the muffins are done, lay a loose sheet of aluminum foil over the top of the pan for the remaining bake time. The muffins are done when a toothpick inserted into the pumpkin batter at the side of a muffin, avoiding the center, comes out with just a few moist crumbs.

Cool in the pan for 5 minutes, then transfer to a wire rack. Do not rush this or the cream cheese center will still be molten and can make the muffin collapse when you move it. Let them sit at least 10 more minutes on the rack before eating so the filling has time to set up properly.