Prep the pan and oven. Heat your oven to 350°F (175°C).
Grease a 9x13-inch baking pan or line it with parchment for easy removal.
Whisk the dry ingredients. In a large bowl, combine 2 1/2 cups flour, 3/4 cup granulated sugar, 1/4 cup brown sugar, 2 1/2 teaspoons baking powder, 1/2 teaspoon salt, 1 1/2 teaspoons pumpkin pie spice, and 1 teaspoon cinnamon. Stir until evenly mixed.
Mix the wet ingredients. In another bowl, whisk 1 cup pumpkin puree, 3/4 cup milk, 2 large eggs, 1/2 cup melted unsalted butter (slightly cooled), and 2 teaspoons vanilla until smooth.
Combine batter. Pour the wet mixture into the dry. Stir with a spatula until just combined.
The batter should be thick but spreadable. Avoid overmixing for a tender crumb.
Spread into the pan. Scrape the batter into your prepared pan and smooth the top.
Make the cinnamon swirl. In a small bowl, mix 1/2 cup softened unsalted butter, 2/3 cup brown sugar, 2 teaspoons cinnamon, and a pinch of salt. Dollop this mixture over the batter in small spoonfuls.
Create the swirls. Use a butter knife or skewer to drag through the dollops in a gentle figure-eight pattern.
Don’t overwork it; you want thick ribbons.
Bake. Bake for 28–35 minutes, until the center is set and a toothpick comes out with a few moist crumbs. If the top is browning too fast, tent with foil for the last 5 minutes.
Cool slightly. Let the cake rest on a rack for 15–20 minutes. This helps it set and makes glazing easier.
Make the glaze. Whisk 1 to 1 1/4 cups powdered sugar with 1–2 tablespoons milk or cream and 1/2 teaspoon vanilla until smooth and pourable.
For a cream cheese glaze, beat 2 ounces softened cream cheese with 1 tablespoon butter, then add 3/4 cup powdered sugar and 1–2 tablespoons milk.
Glaze and serve. Drizzle the glaze over the warm cake. Slice and enjoy warm or at room temperature.