In a small bowl, whisk together 1/4 C. olive oil, vinegar, mustard, salt, and pepper. Cover, and chill.
Preheat grill to medium high heat (350 to 400 degrees).
Pour remaining olive oil in a small bowl. Brush cut sides of romaine lettuce with a small amount of oil. Place romaine, cut side down, on preheated grill. Grill for 1 to 2 minutes, or just until cut side of romaine begins to wilt. Place grilled romaine, cut side up, on each of 4 serving plates.
Brush both sides of zucchini, squash, onion, and tomatoes with a small amount of oil. Place on preheated grill, and grill for 1 to 2 minutes per side, or until vegetables begin to soften. Remove from grill, and place in a large bowl. Add olive oil mixture, tossing gently to coat. Divide vegetables evenly over prepared romaine. Sprinkle each evenly with feta cheese. Serve immediately. Makes about 4 servings.