This dough can also be used for Chocolate-Pecan, Coconut-Lime Oatmeal, Rum-Raisin and Cashew, and Chocolate-Toffee Oatmeal drop cookies.
Preheat oven to 350 degrees. Whisk together flour, baking soda, and salt. In a medium bowl, using a mixer, beat butter and sugars until pale and fluffy, 4 minutes. Add vanilla, eggs, and peanut butter and beat until combined. Add flour mixture and beat until just combined. Mix in cherries.
Drop dough in 2-tablespoon-size balls on parchment-lined baking sheets about 2 inches apart. Bake until cookies are golden around the edges but still soft in the center, 12 to 14 minutes. Let cool on sheets 1 to 2 minutes, then transfer to wire racks and let cool completely.