Preheat the oven to 350°F (175°C).
Drain the jar of maraschino cherries in a colander, rinse them thoroughly, and pat dry on paper towels; finely chop and set aside.
Whisk together the all-purpose flour and baking soda in a medium bowl and set aside.
In a stand mixer or large bowl with an electric mixer, beat the softened butter, packed brown sugar, and granulated sugar on medium speed until smooth and fluffy, about 2 minutes.
Beat in the instant coconut cream pudding mix until incorporated, then add the eggs one at a time, mixing after each.
Add the vanilla and almond extracts and mix to combine.
With the mixer on low speed, gradually add the flour mixture and mix until just combined.
Fold in the chopped maraschino cherries, shredded coconut, and milk chocolate chips until evenly distributed.
Use a medium cookie scoop (about 2 tablespoons) to drop rounded portions of dough onto ungreased baking sheets, spacing them a few inches apart.
Bake in the preheated oven until the edges are golden brown, about 10–12 minutes.
Let the cookies cool on the baking sheets for about 3 minutes, then transfer to a cooling rack with a spatula to cool completely.