In a small saucepan, whisk the brown sugar, milk, and cinnamon together until combined. Heat mixture over medium-high heat, stirring constantly, until mixture begins to boil and sugar has dissolved. Transfer mixture to a shallow bowl and refrigerate until completely cool.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, cream cheese, and vanilla together until smooth and creamy. Add the powdered sugar, and continue beating until combined.

Frost the rim of each glass with the cream cheese frosting, then sprinkle with white chocolate chips, cinnamon chips, and cinnamon sugar. Place glasses in freezer until ready to fill.

To a blender, add the ice cream, milk, and brown sugar syrup. Blend on high until smooth and combined.

Pour milkshake into the prepared glasses. Top each shake with a cinnamon roll, a drizzle of brown sugar syrup, a dollop of whipped cream, and a dash of cinnamon. Insert a couple of straws and sip away!