Preheat oven to 350 degrees. Spray 3 (9-inch) round cake pans with nonstick baking spray with flour. (Or butter and flour each pan.)
In a large saucepan, bring cream to a simmer over medium heat. Add almonds to hot cream and remove from heat. Let stand 30 minutes. Strain almond mixture and reserve cream. (Really press down on almonds with a rubber spatula or the back of a spoon to get as much liquid out as possible.) Place 1/4 cup of the almond cream in a small bowl to reserve for icing. Note from Christin’s post: “I was a little uncertain about making the almond cream because after soaking the almonds in the 2 cups of heavy cream, I ended up with a lot less then 2 cups of almond cream, even after pressing the heck out of the almonds in the strainer. But the recipe doesn’t say how much you should end up with. I was worried I had too little and that I’d end up with a dry cake. I figured I’d rather ere on the side of having too much liquid ingredients rather than too little, so I added in about another 1/4 cup of heavy cream. Because after all, how can you have too much heavy cream?”
In a large bowl, beat butter with an electric mixer at medium-high speed until creamy. Add sugar and beat well. One at a time, add the eggs, stopping to scrape down sides of bowl periodically. Add extracts and beat to incorporate.
In a large bowl, whisk together flour, baking powder, and salt. Gradually add flour mixture to butter mixture, alternating with remaining almond cream, beginning and ending with flour mixture. Beat until combined and divide batter evenly among the 3 pans.
Bake until a wooden pick inserted in the center comes out clean, 23 to 26 minutes. Let cool in pans 5 minutes and remove cakes from pans and let cool entirely on a wire rack.