Cook lasagna noodles for 10 to 12 minutes or till tender but still firm. Drain noodles; rinse with cold water. Drain well.
Meanwhile, for filling, in a large skillet cook ground turkey and onion till turkey is no longer pink and onion is tender. Drain fat. Stir in chopped broccoli and water. Bring to boiling; reduce heat. Cover and simmer about 5 minutes or till broccoli is crisp-tender; drain.
In a mixing bowl stir together egg, ricotta or cottage cheese, and thyme; stir in the turkey mixture. Divide filing mixture into 4 equal portions. Spread a portion over each lasgna noodle; roll up each noodle. Place lasagna rolls, seam side down, in a 2-quart square baking dish. Spoon spaghetti sauce over lasagna rolls.
Bake, covered, in a 375 degree oven about 30 minutes or till heated through. Uncover and sprinkle with the Parmesan cheese. Or, garnish with shaved Parmesan.