Step 1

Place a rack in middle of oven; preheat to 350°. Butter or lightly spray an 8x8" baking pan, 9"-diameter cake pan, or 9x5" loaf pan with unsalted butter or nonstick vegetable oil spray. Line pan with parchment paper, leaving overhang on all sides if using square pan or long side if using loaf pan. Use a parchment paper round on the bottom if using cake pan.

Step 2

Whisk 2 large eggs and ¾ cup (packed; 150 g) light brown sugar in a large bowl until pale and foamy, about 1 minute.

Step 3

Add 1 cup (230 g) unsweetened pumpkin purée, ½ cup extra-virgin olive oil, ½ cup whole milk, 1 tsp. vanilla extract, 1 tsp. ground cinnamon, ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, and a pinch of cayenne pepper (if using). Whisk vigorously until smooth and emulsified.

Step 4

Add ½ cup (45 g) unsweetened Dutch-process cocoa powder and whisk until smooth. Add 1 cup (125 g) all-purpose flour, 1 tsp. baking powder, and ½ tsp. baking soda and whisk again until incorporated. Using a rubber spatula, fold in ½ cup (85 g) bittersweet or semisweet chopped chocolate or chocolate chips.

Step 5

Pour batter into prepared pan; smooth surface with an offset spatula. Tap pan gently on the counter to release any air bubbles.

Step 6

Bake cake until puffed and a tester inserted into the center comes out clean, 45–55 minutes for square or round cake, 55–65 minutes for loaf cake. Transfer cake to a wire rack and let cool in pan 15 minutes. For square or loaf cake, using parchment overhang, lift cake out of pan and onto rack. For round cake, run offset spatula around edges of cake and turn out. Remove parchment and let cool completely.

Step 7

To make the glaze, whisk 1 cup (110 g) powdered sugar, a pinch of ground cloves, a pinch of kosher salt, remaining 1 Tbsp. unsweetened pumpkin purée, remaining 1 Tbsp. whole milk, remaining ¼ tsp. ground cinnamon, and remaining pinch of cayenne pepper (if using) in a small bowl until smooth. Glaze should be pourable. If it’s too thick, whisk in a few more drops of milk.

Step 8

Pour glaze over cooled cake and let sit 20 minutes to allow glaze to set before slicing.

Step 9

Do ahead: Cake can be made 3 days ahead. Store covered at room temperature.