Place the thawed tart cherries, their juices, 120 g sugar, and lemon juice in a medium heavy-bottomed saucepan. Cook over medium heat for 5 minutes, stirring and gently crushing about half the cherries. Stir the cornstarch into the cold water until smooth, then add it to the simmering fruit. Cook for 2 to 3 minutes, stirring constantly, until glossy and thick enough that a spatula leaves a clear trail. Transfer to a shallow container, cover the surface, and refrigerate until completely cold.
Heat a conventional oven to 350°F and position a rack in the center. Grease three 8-inch round pans, line the bottoms with parchment, and lightly grease the paper. Spread the sliced almonds on a small sheet pan and toast for 5 to 7 minutes, stirring once, until pale golden and fragrant; transfer them immediately to a cool plate. In a medium bowl, whisk the all-purpose flour, almond flour, baking powder, and 5 g salt until no almond flour lumps remain.
Fit a stand mixer with the paddle attachment. Beat the softened cake butter and 350 g sugar on medium speed for 4 to 5 minutes, stopping twice to scrape the bowl and paddle, until noticeably paler and increased in volume. With the mixer running on medium-low, drizzle in the oil over about 30 seconds. Continue mixing until the emulsion looks fluffy and uniform rather than greasy. Proper aeration here supports the almond flour and helps the layers rise evenly.
Beat the eggs into the creamed mixture one at a time on medium-low speed, mixing until each disappears before adding the next and scraping the bowl as needed. Whisk the sour cream, milk, vanilla, and 5 ml almond extract together. On low speed, add the dry mixture in three additions, alternating with the milk mixture in two additions, beginning and ending with dry ingredients. Stop when only a few flour streaks remain, then fold by hand until the batter is smooth and evenly blended.
Divide the batter equally among the prepared pans, approximately 530 g per pan, and smooth the surfaces with a small offset spatula. Bake for 23 to 28 minutes, rotating the pans front to back after 18 minutes, until the centers spring back lightly and a tester shows moist crumbs but no wet batter. Cool in the pans on racks for 15 minutes. Run a thin spatula around the edges, invert the layers, remove the parchment, and cool right side up until completely cool, at least 60 minutes.
Combine the egg whites and 300 g sugar in a clean heatproof mixer bowl. Set it over barely simmering water without letting the bowl touch the water, whisking continuously until the sugar dissolves and the mixture reaches 160°F. Whip with the whisk attachment on high for 8 to 12 minutes, until glossy, stiff, and cooled to about 75°F. Switch to the paddle. Add the butter one tablespoon at a time on medium speed, then beat in the vanilla, 2.5 ml almond extract, and 2 g salt until smooth.
Place a cake round or flat serving plate on a turntable. If necessary, trim only the domed tops from the cooled layers with a serrated knife. Set one layer cut side up and pipe a buttercream dam about 3/4 inch high around its edge. Spread half of the cold cherry filling inside the dam without pressing it into the cake. Add the second layer and repeat with another dam and the remaining filling. Place the final layer cut side down, then check the sides from several angles for level alignment.
Use an offset spatula to spread a thin coat of buttercream over the top and sides, filling small gaps where the layers meet. Scrape away excess frosting so the coat is smooth enough to trap crumbs but remains translucent in places. Refrigerate the cake uncovered for 30 minutes, until the buttercream feels firm and the layers no longer shift under light pressure. Keep the remaining buttercream at cool room temperature and stir it gently before applying the final coat.
Cover the chilled cake with the remaining buttercream, smoothing the sides with a bench scraper and the top with an offset spatula. Press the cooled toasted almonds around the lower edge, then arrange the thoroughly dried fresh cherries on top. Refrigerate for 20 to 30 minutes to set the finish. For the cleanest portions, let the cake stand at room temperature for 45 minutes, then cut with a long sharp knife warmed in hot water and wiped dry between slices.