Heat oven to 425°F. Toss broccoli with oil on sheet pan; roast 12 to 15 minutes until tender with dry edges. Cool 5 minutes.
Reduce oven to 350°F; thoroughly butter standard 12-cup muffin pan. Blend eggs, cottage cheese, and pepper smooth; fold in broccoli and ham.
Divide among wells, about three-quarters full. Bake 20 to 24 minutes until puffed, set, and centers 165°F.
Rest 5 minutes; loosen edges and lift to rack. Refrigerate in shallow container within 2 hours. Freeze chilled muffins on lined tray until firm; bag up to 2 months.
For one serving, loosely cover two frozen muffins with damp paper towel on microwave-safe plate. Heat at 50 percent power 1 minute, then full power in 30-second bursts until both centers reach 165°F, usually 1 to 2 minutes more.
Rest 1 minute before eating; centers can be much hotter than surfaces.