Divide ice cream among ice-pop molds, insert sticks, and freeze until firm, at least 4 hours.

Meanwhile, pulse 1 cup cookies in a mini food processor until fine crumbs form. Transfer crumbs to a plate. Add strawberries to remaining crumbs in food processor and pulse a few times to create strawberry crumbs. Stir strawberry crumbs into plain crumbs on plate.

Line a rimmed baking sheet with parchment paper. Dip molds briefly into hot water. Working one at a time, remove ice pops from mold, one at a time, and thaw briefly. Dip in crumbs, turning to coat, sprinkling crumbs over pops if necessary, and pressing to adhere. Transfer pops to prepared baking sheet and freeze again at least 30 minutes before serving.