Preheat oven to 350°F. Grease an 8x8-inch baking dish and line with parchment paper. Set aside.

To make the brown butter, add the butter to a light-colored saucepan over medium heat. Melt the butter, then continue cooking while stirring frequently. The butter will foam, and the milk solids will begin to turn golden brown. Once it smells nutty and toasted and the butter reaches a deep golden color, remove it from the heat. Pour the brown butter into a heat-safe bowl, making sure to scrape in the browned bits from the bottom of the pan. Let cool completely before using.

In a large bowl, whisk together the cooled brown butter, brown sugar, granulated sugar, eggs, and vanilla. Whisk in the pumpkin puree and Greek yogurt until smooth.

In a separate bowl, combine the flour, baking powder, baking soda, pumpkin pie spice, cinnamon, and salt. Gently fold the dry ingredients into the wet ingredients until just combined. Don’t overmix. Pour the batter into the prepared baking dish and spread evenly.

In a medium bowl, make the streusel. Combine the flour, brown sugar, cinnamon, and salt. Stir in the melted butter until crumbly. Sprinkle evenly over the batter.

Bake for 46-48 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Let cool for at least 15 minutes.

While the coffee cake cools, make the glaze. Whisk together the powdered sugar, caramel sauce, milk, and vanilla. Drizzle over the slightly warm or cooled coffee cake.