Line a 12-cup muffin pan with 6 muffin liners and set it aside. Preheat the oven to 425°F (220°C).

Combine the brown sugar, cinnamon, flour, and melted butter until combined and crumbs form. Spread onto a lined baking sheet. Chill in the freezer for at least 30 minutes, then break into pea-sized pieces before using.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a separate large mixing bowl, whisk together the buttermilk, sugar, melted butter, eggs, sour cream, oil, and vanilla. Whisk the dry ingredients into the wet ingredients until almost combined, with some flour streaks still remaining. Then fold in the cinnamon crumb mixture.

Scoop about 1/3 cup of the batter into each cup of the lined muffin tray. The batter should fill higher than the muffin liner.

Bake at 425°F for 8 minutes, then without opening the oven door, decrease the temperature to 350°F (180°C) and bake for another 10-18 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs and the tops are golden brown.

Let the pan cool on a wire rack for 10 minutes, then carefully remove the muffins from the pan. Repeat with the remaining batter (6 muffins).

To make the cream cheese icing, combine the cream cheese and powdered sugar. Whisk in the milk and vanilla until smooth.

Dunk the tops of the cinnamon roll muffins with the glaze or drizzle it over the top.