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HEAT oven to 375°F.
MELT butter in large skillet on medium-high heat. Add onions; cook and stir 3 min. Add mushrooms, carrots and garlic; cook and stir 6 min. or until carrots are crisp-tender. Add flour; cook and stir 2 min. Gradually stir in milk. Bring to boil, stirring frequently. Remove from heat. Stir in spinach, 1 cup cheddar and Parmesan.
MIX cottage cheese and basil. Place 3 lasagna noodles on bottom of 13x9-inch baking dish sprayed with cooking spray; top with layers of half the cottage cheese mixture and 2 cups vegetable mixture. Cover with 3 noodles, remaining cottage cheese mixture and 2 cups vegetable mixture. Top with remaining noodles and vegetable mixture; cover.
BAKE 35 to 40 min. or until heated through. Top with remaining cheddar; bake, uncovered, 5 min. or until melted. Let stand 10 min. before serving.