Whisk flour, baking powder, baking soda, and salt in medium bowl.
In second medium bowl, stir together oats, pecans, cherries, and chocolate.
In standing mixer fitted with flat beater, beat butter and sugar at medium speed until no sugar lumps remain, about 1 minute.
Scrape down sides of bowl with rubber spatula; add egg and vanilla and beat on medium-low speed until fully incorporated, about 30 seconds.
Scrape down bowl; with mixer running at low speed, add flour mixture; mix until just combined, about 30 seconds.
With mixer still running on low, gradually add oat/nut mixture; mix until just incorporated.
Give dough final stir with rubber spatula to ensure that no flour pockets remain and ingredients are evenly distributed.
Divide dough evenly into 16 portions, each about 1/4 cup, then roll between palms into balls about 2 inches in diameter; stagger 8 balls on each baking sheet, spacing them about 2 1/2 inches apart.
Using hands, gently press each dough ball to 1 inch thickness.
Bake both baking sheets 12 minutes, rotate them front to back and top to bottom, then continue to bake until cookies are medium brown and edges have begun to set but centers are still soft (cookies will seem underdone and will appear raw, wet, and shiny in cracks), 8 to 10 minutes longer.
Do not overbake.
Cool cookies on baking sheets on wire rack 5 minutes; using wide metal spatula, transfer cookies to wire rack and cool to room temperature.