Combine oats, sesame seed, and almonds in a 10- by 15-inch rimmed pan. Bake in a 350° oven, stirring occasionally, until nuts begin to brown, about 20 minutes (about 15 minutes in a 325° convection oven).
In a 4- to 5-quart pan over low heat, melt 3/4 cup butter. Remove from heat and add honey, brown sugar, and nutmeg; stir until blended. Stir in oat mixture, apricots, raisins, and coconut.
Butter and flour the 10- by 15-inch pan. Scrape oat mixture into pan; press firmly into an even layer.
Bake in a 350° oven until evenly browned and bubbly in center, 20 to 25 minutes (10 to 15 minutes in a 325° convection oven).
Cool on a rack 20 minutes. Cut into 2- by 5-inch bars. When cool, lift from pan with wide spatula.