For the cinnamon streusel:
1 cup packed brown sugar
2 teaspoons ground cinnamon
For the cake:
3 cups all-purpose flour
1 tablespoon pumpkin pie spice
2 teaspoons baking powder
1 teaspoon baking soda
1/4 teaspoon fine salt
1 cup (2 sticks) unsalted butter, at room temperature
2 cups granulated sugar
3 large eggs
1 (15-ounce) can pumpkin purée (not pumpkin pie filling)
1 teaspoon vanilla extract
For the salted caramel sauce:
1/3 cup granulated sugar
1 tablespoon water
1/2 cup heavy cream, at room temperature
1 tablespoon unsalted butter
1/2 teaspoon fine salt
Arrange a rack in the middle of the oven and heat to 350°F. Generously butter and flour the sides and tube of a 12-cup Bundt pan or coat with cooking spray; set aside.
Make the cinnamon streusel: Mix the sugar and cinnamon together in a small bowl; set aside.
Make the cake: Whisk together the flour, pumpkin pie spice, baking powder, baking soda, and salt in a medium bowl.
Place the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, use a large bowl and hand mixer.) Beat on medium-high speed until fluffy and lightened in color, about 3 minutes. Add the eggs one at a time, beating until each is incorporated. Beat in the pumpkin purée and vanilla extract, scraping down the sides of the bowl as needed.
With the mixer on low speed, add the flour mixture and beat lightly, just until flour is no longer visible.
Transfer half of the batter to the prepared Bundt pan and spread into an even layer. Sprinkle the cinnamon streusel over the batter in an even layer. Top with the remaining batter.
Bake until the cake springs back to a gentle touch and a toothpick inserted into the center comes out clean, 55 to 60 minutes. Cool for 10 minutes in the pan on a wire rack. Flip the cake out onto the rack and cool completely. While the cake cools, prepare the salted caramel sauce.
Make the caramel: Heat the sugar and water over high heat in a medium saucepan, stirring until the sugar is dissolved. Cook undisturbed until the sugar turns golden-brown, 8 to 10 minutes. Remove the pan from the heat and pour in the cream. Be careful, as the mixture will sputter and bubble up. Whisk until the bubbling subsides.
Add the butter and salt and whisk until they're fully incorporated. Set the sauce aside and cool to room temperature, about 30 minutes. It will thicken as it cools. Transfer the sauce to a jar, seal, and store in refrigerator until ready to serve with the cake.