Directions:

1. Preheat oven to 350 degrees. Grease three 8-by-2-inch round cake pans and line with greased parchment paper circles.

2. Make burnt sugar syrup: Place sugar in a small saucepan or sauté pan that is very clean. Over medium heat, swirl patiently (do not stir) until sugar is melted and amber in color. (Sugar will smoke.) Remove pan from heat and add hot water, a few drops at a time, taking care, as sugar will spatter. Once all water has been added, put pan back over medium heat and cook to reduce syrup, stirring occasionally with a wooden spoon to incorporate any sugar stuck to bottom of pan, 5 minutes. Remove the syrup from the heat and allow it to cool for 10 minutes.

3. Make cake: In a small bowl, sift together flour, baking powder and salt, then whisk mixture to ensure that ingredients are well mixed. Set aside.

4. In the bowl of a stand mixer fitted with paddle attachment, cream butter, sugar and maple syrup on medium-high speed until fluffy, about 5 minutes. As you make batter, stop mixer frequently and scrape down paddle and sides of the bowl. With mixer on low speed, drizzle oil and vanilla into mixture until well combined. Blend in eggs and yolks one at a time, adding each as soon as previous one has disappeared into batter.

5. In a small bowl, combine milk and burnt sugar syrup. With mixer on low speed, add one-third flour mixture, then one-half milk-syrup mixture, and repeat, alternating between the two mixtures. Aftereach addition, mix until just barely blended, stop and scrape down sides of bowl. Stop mixer before the last of flour mixture has been incorporated and complete blending by hand with a rubber spatula.

6. Divide batter evenly among prepared pans and smooth tops. Bake until cakes are golden and centers spring back when lightly touched, 28-30 minutes. Right after you remove cakes from oven, run a thin knife around edges of cakes. Cool cakes in pans on a wire rack for 30 minutes. Turn cakes out of pans, leaving on parchment paper until you assemble cake. Let cakes cool on rack to room temperature, top sides up.

7. Make frosting: In the bowl of a stand mixer fitted with paddle attachment, beat butter on medium speed until smooth, about 1 minute. Add cream cheese and continue beating until frosting is smooth and lump-free, about 1 minute more. Dissolve espresso powder in vanilla and blend this mixture into frosting. Blend in maple syrup. Continue mixing on medium-high speed, scraping bowl as necessary to rid frosting of any lumps,until frosting is well blended and smooth. If frosting is too soft to work with, place it in refrigerator to firm up. (Frosting keeps in refrigerator for up to 7 days. If refrigerated, frosting will need to be brought back to room temperature and rewhipped before using.)

8. Assemble cake: Lay one layer top-side up on a flat plate. Using a metal spatula, frost top with 3/4 cup cream cheesefrosting, spreading it out to edge of cake. Stack second layer top side up on top of frosted cake and spread another 3/4 cup frosting on top. Stack last layer of cake, also top-side up, on top. Apply thin layer of frosting all over. Place cake in refrigerator until frosting is firm, about 15 minutes. Take cake out and frost with remaining frosting. Cake should be served at room temperature. Cake can be stored up to 4 days in refrigerator in an airtight container. Remove from refrigerator at least 1 hour before serving.