Beat softened butter on high speed with a mixer until creamy, about 1 minute.
Add sugar, vanilla, and almond extracts on medium speed, scraping bowl sides and bottom as needed.
Slowly drizzle in cherry juice on high speed and beat for 1 minute.
Turn mixer to low speed and gradually add flour until a very soft dough forms.
Add chopped maraschino cherries, mixing just until evenly dispersed.
Press dough into a compact disk, cover tightly with plastic wrap, and chill until firm, at least 4 hours or up to 3 days.
Preheat oven to 350°F (177°C). Line baking sheets with parchment paper or silicone mats.
Shape dough into smooth 1 Tablespoon-sized balls and refrigerate if sticky or soft before baking.
Bake cookies for 10-12 minutes until edges are lightly browned.
Cool cookies on the baking sheet for 5 minutes, then transfer to a wire rack to cool at least 30 minutes.
Melt white chocolate in a double boiler or microwaving in 20-second intervals, stirring until smooth.
Drizzle melted white chocolate over cooled cookies using a squeeze bottle or spoon.