Preheat the oven to 350 degrees F. Line a large baking sheet with parchment paper.
Toast the almonds: Place sliced almonds on the baking sheet and toast in the oven until golden brown, fragrant and crunchy, stirring halfway through, 10 to 13 minutes total. Set aside to cool for 5 minutes. Keep heat in the oven.
Mix the wet ingredients: In the bowl of a stand mixer fitted with the paddle attachment, mix the butter, brown sugar and granulated sugar on medium speed until well combined, about 2 minutes. Add the egg, egg yolk, amaretto, and almond extract and mix again on medium speed until smooth and creamy, about 1 minute.
Add the dry ingredients: Add the flour, oats, baking soda, and salt and mix on medium-low speed until just combined, about 1 minute. Add ½ cup (50 grams) toasted almonds (the remaining will be used as a garnish) and mix on low speed until just incorporated into the dough, 30 seconds.
Roll 2 tablespoons of dough into a ball and place on the prepared baking sheet. Repeat with more dough, placing the balls 2 inches apart, until you’ve filled up the baking sheet. (Not all cookies will fit on the sheet in one batch.) If for some reason, the dough is too wet and you have an issue with spreading, cover the dough and chill the dough for 1 hour in the fridge.
Bake the cookies: Bake until the cookies are just golden brown on the edges, 10 to 13 minutes. Cool the cookies on the sheet for 5 to 10 minutes, then transfer to a wire rack to finish cooling. Once the baking sheet has cooled, repeat with remaining dough.
While the cookies cool, cook the cherries: In a small pot, combine the cherries and sugar and place over medium heat. Cook, stirring frequently, and mashing cherries down with the back of a wooden spoon, until the cherries break down and release their juices and the mixture slightly thickens, about 5 minutes. Remove the pot from the heat.
Make the icing: Place a small sieve over a medium bowl. Add cherry filling to the sieve and use a spoon to mash down the filling. This will strain out any large pieces of cherries. You should have about 1 to 2 tablespoons of cherry liquid. In the same medium bowl as the cherry liquid, add the powdered sugar, milk and almond extract and whisk until a thick icing forms. Add more milk to thin, a teaspoon at a time, if the icing is too thick.
Ice the cookies: Spoon 2 teaspoons of icing on top of each cookie and spread out as best as you can with a spoon, then return to the wire rack and immediately sprinkle with a few toasted almonds on top. Allow icing to harden completely before enjoying, about 10 minutes.