Heat oven to 375°F (190°C). Use the softened unsalted butter to thoroughly grease a 9x13-inch baking dish (or a similar 2-quart pan), ensuring all corners and sides are covered to avoid sticking and to add flavor.
Arrange the pitted cherries evenly across the bottom of the buttered dish in a single layer. Since they'll settle during baking, spread them out so each serving gets a cherry.
In a blender, place the room-temperature eggs, whole milk, heavy cream, all-purpose flour, 1/3 cup sugar, vanilla extract, almond essence, salt, and lemon zest. Process on medium speed for 30-45 seconds, stopping once to scrape down the sides, until the mixture is silky and free of lumps. The batter should be thin and pourable, akin to crêpe batter.
Pour the batter over the cherries, making sure it's distributed evenly. Bake at 375°F (190°C) for 30-40 minutes, or until the top is golden and puffy, and a toothpick inserted into the center comes out clean or with a small amount of custard clinging. The clafoutis will rise significantly, then deflate a bit upon cooling.
Take out of the oven and allow to rest at room temperature for 5-10 minutes so it sets properly without becoming tough. If desired, sprinkle powdered sugar over the top before serving. Serve warm or at room temperature, accompanied by whipped cream, crème fraîche, or vanilla custard.