Soften stick of butter and add dry ingredients, along with crushed garlic, then wrap in foil and freeze for 30 minutes. Shape ground beef into 4 large patties. Remove herb butter from freezer along with ice cubes. Crush ice cubes to get 4 small chunks. Slice herb butter into 4 1-inch slices.
Return remainder to freezer.
Place on hot grill and grill 15 minutes each side, turning often after first 10 minutes. Serve on Sesame seed roll.