Preheat the oven to 375 degrees F and line baking sheets with parchment paper.Place the butter, brown sugar and granulated sugar in a large mixing bowl and beat on medium-high speed until very pale and fluffy (3 to 5 minutes minimum).
Add the egg, egg yolk, and vanilla, beating until completely incorporated.
Scrape the bottom and sides of the bowl with a silicone spatula, then add the flour, cornstarch, baking soda, and salt, stirring on medium-low speed just until all the ingredients are combined (do not over-mix).
Stir in the chocolate chips, cherries, and almonds.
Use a 2-tablespoon scoop to drop balls of cookie dough onto the prepared sheets, allowing about two inches in between (for spreading).
Bake (one sheet at a time) on the center rack of the oven until set around the edges and just barely beginning to turn golden (approx. 8 to 10 minutes).
Cool completely on the baking sheet, then transfer to an air-tight container for storage.
Notes
Regular chopped almonds can be used in place of the slivered almonds.