Mash eggs, avocado, olive oil, garlic, and lemon-pepper seasoning together in a bowl until sauce is smooth. Add cabbage and Greek yogurt to sauce and toss until evenly coated. Mix onion, sunflower seeds, and broccoli into cabbage mixture until evenly coated. Mix lemon juice, salt, and pepper into slaw. Cover bowl with plastic wrap and refrigerate until chilled, at least 30 minutes.
