Preheat oven to 325°F (170°C).

For filling: In a small bowl, stir together flour, brown sugar, espresso powder, cinnamon, and salt. Add butter, and rub in by hand until mixture is sandy and well combined.

For batter: In a large bowl, whisk together pumpkin, brown sugar, granulated sugar, crème fraîche, oil, melted butter, eggs, and vanilla bean paste.

In a medium bowl, whisk together flour, baking powder, salt, nutmeg, pie spice, cinnamon, and baking soda. Gradually whisk flour mixture into pumpkin mixture until smooth and well combined.

Spray a 10-cup Bundt pan with baking spray with flour. Spoon one-third of batter into prepared pan (about 2¼ cups or 567 grams). Tap pan on a kitchen towel-lined counter several times to settle batter and release any air bubbles. Using a small spoon, sprinkle half of filling (3½ to 4 tablespoons or about 43 grams) in a ring on top of batter in pan, layering and spreading mixture as needed and leaving about a ¼-inch border around edges. Top with one-third of batter. Tap on a kitchen-towel-lined counter a few times to settle batter and release any air bubbles. Top with a ring of remaining filling; cover with remaining batter. Tap on a kitchen towel-lined counter several times to settle batter and release any air bubbles.

Bake for 55 minutes. Rotate pan, loosely cover with foil, and bake until a wooden pick inserted near center comes out clean and an instant-read thermometer inserted near center registers 200°F (93°C) to 205°F (96°C), 20 to 25 minutes more. Let cool in pan for 15 minutes. Invert cake onto a wire rack, and let cool completely.

For topping: In a small bowl, stir together granulated sugar, brown sugar, cinnamon, espresso powder, and nutmeg. Brush cake with melted butter; cover with sugar mixture, pressing gently to help adhere, if needed. Serve immediately.