Gluten Free Vegetarian Lasagna

I found this recipe online many years ago. I haven't tried it...this is my continuing quest to find a great vegetarian lasagna. The portions mentioned in the recipe were off, in my opinion. So I have amended them here.

6 carrots, sliced and steamed
Large bundle of mixed greens, dry sauteed (using the water from the leaves only)
8 mushrooms, sliced and sauteed with 3 cloves of chopped garlic
2 1/2 C milk
2 T butter
6 T corn starch
salt and pepper
Cheese
GF lasagna noodles

Keep the vegies in separate groups. Melt the butter in a saucepan. Take off the heat and stir in the cornstarch. Put back on the heat and slowly add the milk, stirring constantly (medium-high heat) until mixture is thickened. Add salt and pepper to taste.

Preheat oven to 350. Put lasagna noodles in the bottom of your baking dish. Put 1/3 of the white sauce on the noodles. Layer with 1/2 each of the three different vegies. Add another layer of noodles, 1/3 of the sauce, and last half of the vegies. Finish with a noodle layer, the last of the white sauce, and then cheese to suit your taste.

Bake for 40 minutes.

**I used 2% milk. This was an easy recipe but wasn't outstanding.