Drain maraschino cherries through a fine-mesh strainer, then spread on paper towels and pat thoroughly dry. Finely chop into 1/4-inch pieces, place on fresh paper towels to continue draining, and preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
Beat softened butter, granulated sugar, and brown sugar together on medium speed for 3–4 minutes until light, fluffy, and pale, scraping down the bowl as needed.
Add eggs one at a time, beating well after each addition, then mix in vanilla extract, almond extract, and pink gel food coloring (if using) until smooth and evenly combined.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt for at least 30 seconds to ensure even distribution of leavening agents.
With mixer on low, add flour mixture to the wet ingredients in three additions, mixing after each just until no dry streaks remain. The dough should be thick and slightly sticky; do not overmix.
Using a rubber spatula, gently fold the chopped cherries and chocolate chips into the dough until evenly distributed, being careful not to overmix or break up the cherries.
Scoop 2-tablespoon portions of dough onto prepared baking sheets, spacing them 2–3 inches apart. Optionally press a few extra chocolate chips on top for a bakery-style look.
Bake one sheet at a time for 11–13 minutes, rotating halfway through, until edges are set and lightly golden while centers still look slightly underdone. Remove from oven and rest on the pan for 5 minutes.
Transfer cookies to a wire rack and cool completely for 20–30 minutes before storing. Repeat with remaining dough, ensuring the baking sheet has cooled before adding new dough balls.