In medium-size bowl, combine eggs and flour. Whisk in milk until smooth. Let stand 30 minutes.
Meanwhile, in a food processor, pulse together the onion, garlic and mushrooms until coarsely chopped.
Coat 10-inch skillet with nonstick cooking spray. Heat skillet over medium-high heat. Add mushroom mixture, salt, Italian seasoning and pepper; saute 3 minutes. Add drained chopped spinach; saute 3 minutes. Remove from heat and let cool slightly. Stir in ricotta cheese, 3/4 cup of the mozzarella cheese and the Parmesan cheese.
To prepare cannelloni wrappers, coat 7- or 8-inch nonstick skillet with nonstick cooking spray. Heat over medium heat. Pour in 2 tablespoons batter, rotating skillet quickly to spread batter evenly over bottom; cook until top is dry but bottom is not brown, about 1 minute. Turn wrapper over; cook 15 seconds longer. Transfer to waxed-paper-lined plate; top with sheet of waxed paper. Repeat with remaining batter for a total of 12, stacking wrappers between sheets of waxed paper. (Wrappers can be prepared a day or two ahead, wrapped and refrigerated.)
Heat oven to 350 degrees F.
Spoon 1 cup marinara sauce over bottom of 13 x 9 x 2-inch baking dish. Spread 1/4 cup filling down center of each cannelloni wrapper; roll up. Place cannelloni, seam side down, in baking dish. Spoon the remaining sauce over top of cannelloni. Sprinkle evenly with the remaining 1/4 cup shredded mozzarella cheese.
Bake, uncovered, in 350 degree F oven until the filling is bubbly, 30 to 40 minutes. Makes 6 servings.