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