This rich, golden cake is deeply flavored and irresistibly moist. It makes a stunning holiday dessert.
Have all ingredients at room temperature, about 70°F. Preheat the oven to 350°F. Coat a 9-inch Bundt pan with cooking spray.
Combine in a medium saucepan:
Bring to a simmer over medium-high heat, then cover, take off the heat, and let sit for 30 minutes. Melt in a medium skillet:
Cook over medium heat until the butter crackles and foams and the milk solids turn golden brown (keep a close eye on it, as it can burn quickly). Immediately transfer the brown butter to a large mixing bowl or a stand mixer with the paddle attachment, using a spatula to scrape the brown bits on the bottom of the skillet into the bowl. Beat on medium-low speed until cooled. Sift together into a medium bowl:
Add to the cooled browned butter and beat until smooth:
Beat in:
Beat in one at a time:
Add the flour mixture to the butter mixture in 2 parts, alternating with:
Beat until just combined. Fold in the figs along with any unabsorbed Cognac. Scrape the batter into the prepared pan. Bake until a toothpick inserted into the center comes out clean, about 45 minutes.
Let cool in the pan on a rack for 30 minutes. Invert onto the rack to cool completely. Serve with: