Line an 8-by-8-inch baking pan with parchment paper, leaving a 2-inch overhang. In a food processor, finely grind 1/2 cup oats; place in a medium bowl. Stir in the remaining 1 cup oats, the cherries, almonds, allspice and 1/8 tsp. salt.
In a large bowl, mix the almond butter and honey. Fold in the oat mixture; mix until well combined, using your hands, if needed.
Scrape the mixture into the baking pan. Using the back of a measuring cup, press down firmly, creating a compact, even layer. Refrigerate until set, at least 8 hours or overnight.
Lift the bars out of the pan. Cut into eight 2-by-4-inch rectangles.