Heat the oven to 350°F (175°C). Place the silicone mold on a rimmed baking sheet to keep it even. If using a standard metal muffin tin, lightly butter and flour the wells. Set aside.
Beat the 1 stick unsalted butter, 1/2 cup packed dark brown sugar, and1/4 cup granulated sugar in the bowl of a stand mixer using the beater attachment until fluffy, about 5 minutes.
Meanwhile, whisk together 3/4 cup all-purpose flour, 1/2 cup Dutch-processed cocoa, 1/2 teaspoon baking soda, and 1/8 teaspoon salt in a medium bowl, and set aside.
With the mixer running, plop the 1 large egg then the 1 large egg yolk, into the creamed butter-sugar mixture, scraping the bowl after each addition. Add the 1/4 cup sour cream and 1/2 teaspoon chocolate extract, if using, and mix until combined.
Alternate adding the dry ingredients with the 1 teaspoon powdered instant coffee dissolved in 2/3 cup boiling water in 3 additions, beginning and ending with the dry ingredients.
Divide the batter evenly among the molds (or muffin tin), filling them almost to the top.
Bake until a toothpick inserted in the center comes out clean, 20 to 25 minutes. Set the mold on a wire rack and let cool for 5 minutes. Run the tip of a knife around the rim of each cake and lift out. Place the cakes, flat-side down, on the wire rack to cool completely.