Makes one 9-inch cake

For the cake:

1 2/3 cups all-purpose flour
1 1/2 teaspoons baking powder
1/2 teaspoon baking soda
1 tablespoon plus 1 teaspoon ground cinnamon
1 teaspoon freshly grated nutmeg
1/4 teaspoon ground cloves
1 cup plus 2 tablespoons (9 ounces) pumpkin purée
1 cup vegetable or canola oil
1 1/3 cups sugar
3/4 teaspoon salt
3 large eggs, at room temperature, yolks and whites separated

For the frosting and the caramelized pumpkin seeds:

9 tablespoons butter, divided, at room temperature
8 ounces cream cheese, at room temperature
2 1/2 cups powdered sugar
Pinch of cinnamon
1 tablespoon sugar
1/2 cup pumpkin seeds (raw or toasted)