Over medium heat, sauté potato cubes and green bean in 1 Tbsp butter until crisped, about 5 minutes. Remove, toss with pine nuts and parsley, season with salt and pepper and set aside.
In same saucepan, heat remaining butter and add zucchini and cherry tomatoes. Pour in eggs and cook until set, about 4 minutes. Fold omelet in half and cut into two pieces. Place omelet pieces on bottom of bagel, add potato cube mixture, parmesan cheese, and top with bagel top.