First, make the dumplings: Place 1 wonton wrapper on work surface. Place a second wrapper on top, at a 1/4 turn, to make a star pattern. Put 1 cheese cube in the middle: Moisten wontons all around cheese with water and fold up, bringing edges together and pressing to seal just above the cheese. The edges should look sort of ruffled, like a paper bag that has been gathered in the middle: Repeat with remaining wrappers and cheese.
Bring 2 quarts water to a boil, add half of dumplings and cook, boiling, for 1 minute. Remove with a slotted spoon and set aside. Repeat with second half of dumplings.
For the mushrooms and spinach: Coat a large nonstick skillet with grapeseed oil spray, add sesame oil and heat over medium-high heat until hot. Add garlic, carrots and green onions and sauté for 2 minutes. Add mushrooms and sauté until tender. Stir in spinach, cover and cook 1 to 2 minutes or until spinach wilts. Toss with 1 tablespoon of the soy sauce, remove from heat and keep warm.
In the same skillet, arrange dumplings in a single layer. Combine remaining 2 tablespoons soy sauce with 3 tablespoons water and pour over top. Bring to a boil, reduce heat to medium-high and cook, uncovered, turning the dumpling periodically to cook on all sides. Cook until most all of the liquid has evaporated, around 2 to 3 minutes.
Spoon spinach mixture onto individual dinner plates, top with dumplings and sprinkle with sesame seeds.