Preheat the oven to 350°F (175°C). Line a sheet pan with a large piece of foil, leaving plenty of overhang on all sides. Don't wrap the foil around the pan yet; you'll pull it up around the cake later while it bakes.

Spray a 9-inch round cake pan generously with baking spray. Use a paper towel to spread the spray evenly over the bottom and sides. Spray the bottom lightly one more time, then line it with a round of parchment paper. The extra spray helps keep the parchment securely in place.

If using coffee (highly recommended), brew ½ cup and set aside to cool.

In a medium bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt.

Make a well in the center of the dry ingredients and add the milk, oil, egg, vanilla, and cooled coffee. Whisk until the batter is smooth and well combined. The batter will be thinner than most cake batters; that's exactly what you want.

Pour the batter into the prepared cake pan and set aside.

In a clean medium-large bowl (I just wash out the same bowl), whisk together the ricotta, sugar, eggs, vanilla, and salt until smooth and creamy.

Scoop up the ricotta mixture and pour it over the chocolate batter, beginning around the outer edge of the pan and working toward the center. Try to cover as much of the chocolate batter as possible, but don't worry if a few small spots remain uncovered.

Place the cake pan on the foil-lined sheet pan, leaving the foil flat for now. Bake for 35 minutes.

Carefully pull the foil up around the sides of the cake pan. This simple step helps keep the cake moist and prevents the edges from drying out.

Continue baking for 20–25 minutes, or until the center no longer jiggles when gently shaken. A toothpick inserted in the center should come out clean, but the most reliable way to test for doneness is with an instant-read thermometer. The center of the cake should register 200–205°F (93–96°C).

Let the cake cool in the pan for 20 minutes, then carefully invert it onto a parchment-lined cooling rack. (The parchment prevents the warm cake from sticking to a cooling rack and protects its beautiful surface.) Peel off the parchment from the cake and discard it.

Allow the cake to cool completely. Once cooled, invert the cake again onto a serving platter or cake stand and frost.

In a medium bowl, whisk together the powdered sugar and cocoa powder. Set aside.

Place the softened butter in a medium-large bowl and whisk vigorously for 30-45 seconds until smooth and creamy.

Slowly whisk in the half-and-half, corn syrup, and vanilla. Whisk until silky smooth.

Set a fine-mesh sieve over the bowl. Add about half of the powdered sugar mixture to the sieve and sift it into the butter mixture, tapping gently as needed. (I like to use a metal spoon or small whisk to stir the powdered sugar mixture in the sieve, which helps it sift more quickly.)

Stir with a spatula until smooth and creamy. Sift in the remaining powdered sugar mixture, discarding any small lumps left in the sieve. Stir until completely incorporated and smooth.

The frosting should be soft, creamy, and easily spreadable. If it's too thick, add additional half-and-half, 1 teaspoon at a time, until it reaches the perfect consistency. If it's too thin, add a little more powdered sugar until thickened.