Preheat oven to 350°F. Grease and line an 8x8-inch square pan with parchment.
Make the cinnamon swirl: Stir together brown sugar, granulated sugar, cinnamon, and melted dairy-free butter until sandy. Set aside.
Make the pumpkin cake: In a medium bowl, whisk together flour, baking powder, baking soda, salt, and spices. In a large bowl, whisk pumpkin puree, both sugars, oil, eggs, and vanilla until smooth. Fold in dry ingredients until just combined.
Spread half the batter into the prepared pan. Sprinkle half the swirl mixture over it. Repeat with remaining batter and swirl mixture, finishing with dollops on top. Use a butter knife to marble it slightly.
Bake 35–40 minutes, until a toothpick comes out mostly clean (a few moist crumbs are fine).
Make the glaze: Beat cream cheese and butter until creamy. Add powdered sugar, vanilla, and just enough milk for a drizzle consistency.
Once cake is cool, drizzle glaze over the top. Slice and enjoy!