Blend carrots, canola oil, onion, 1 teaspoon salt substitute, and pepper together in a blender until smooth. Whisk water and cornstarch together in a bowl until cornstarch is dissolved; add to carrot mixture and blend until smooth. Pour carrot mixture into a 1 1/2-quart casserole dish and press into a 'crust' shape.
Bake in the preheated oven until crust is dry and firm, about 20 minutes.
Whisk broccoli, eggs, pesto, and 1 teaspoon salt substitute together in a bowl until smooth; pour over the carrot crust.
Bake in the preheated oven until set in the middle, 40 to 45 minutes. Cool quiche for 25 minutes and top with Parmesan cheese.