Preheat your oven to 375°F (190°C) and prepare a 12-count muffin tin by lining it with paper liners.
In a small bowl, smooth out the softened cream cheese using a spatula. Mix in granulated sugar and vanilla extract, stirring until creamy and uniform. Set aside.
In a separate large bowl, beat softened butter with both the granulated and brown sugars until the mixture is fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the pumpkin puree and vanilla extract. Once incorporated, pour in the milk and blend again.
In another bowl, whisk together the flour, pumpkin spice, ground cinnamon, baking powder, baking soda, and salt. Gradually fold the dry mixture into the wet ingredients using a spatula. Be careful not to overmix; stir just until everything is combined.
Spoon about 2 tablespoons of the pumpkin muffin batter into each muffin liner. Use the back of a spoon to create a small well in the center. Fill each well with a heaping tablespoon of cream cheese filling. Cover the filling with more pumpkin batter, filling the liners about ¾ full.
Combine the flour, sugars, and cinnamon in a small bowl. Drizzle in melted butter and use your hands or a fork to mix until crumbly. Evenly distribute the streusel over the muffins.
Bake in the preheated oven for 23-25 minutes, until the muffin tops start to turn golden and a toothpick inserted into the center comes out with a few dry crumbs. Let the muffins cool before serving.