Preheat the oven to 350°F. Line baking sheets with parchment paper and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine ½ cup butter (room temperature), ½ cup sugar, and ½ cup brown sugar. Beat on medium speed until light and fluffy, about 2–3 minutes.
Add 1 egg and 2 teaspoons vanilla. Beat just until combined, stopping once the mixture is uniform and scraping down the sides of the bowl as needed.
Add 1 ½ cups flour, ½ teaspoon baking soda, and ¼ teaspoon salt to the bowl. Mix on low speed until the dry ingredients are just incorporated; do not overmix.
Fold in ¾ cup coarsely chopped white chocolate, ½ cup coarsely chopped milk chocolate, 1 cup dried tart cherries, and ½ cup coarsely chopped pecans. Do this with the mixer on low for a few seconds or by hand with a wooden spoon until evenly distributed.
Using a tablespoon or a cookie disher, scoop rounded tablespoonfuls of dough and place them about 2 inches apart on the prepared baking sheets.
Gently press each mound of dough with the heel of your hand to slightly flatten the tops so they spread evenly while baking.
Bake in the preheated oven until the cookies are just set and lightly golden around the edges, about 12 minutes.
Let the cookies cool on the baking sheets for about 5 minutes, then transfer them to a wire rack to finish cooling.