Preheat oven to 375°F. Spray or rub oil into 8×8-inch baking dish.
For vegetables:
Place frozen kale in a microwave-safe measuring cup (or small bowl) and thaw in microwave on high, for 1 to 2 minutes. (Alternatively add frozen kale to skillet as indicated below, but cook a little longer.)
Chop onion (to yield about 1 cup). Melt butter in a large skillet over medium-low heat and add onion. Cook and stir while you continue. Lower heat if needed.
Slice cherry tomatoes into halves or quarters. (If using a large tomato, cut in halves or quarters then gently squeeze out some of the juices and scrape out most of the seeds before chopping.) Drain excess juices. Add tomatoes to skillet. Cook and stir while you continue.
Mince garlic and add to skillet. Cook another minute.
Stir in chopped kale and continue cooking until most of the moisture has evaporated, about 3 to 5 minutes. Remove from heat.
For egg mixture:
While vegetables cook, break eggs directly into baking dish (to save on dirty dishes). Add pesto, salt, nutmeg, and red pepper flakes, then beat lightly with a fork (or whisk).
Measure about 1/4 cup milk in a liquid measuring cup. Stir in flour until dissolved and smooth. Add more milk to reach the 1-cup mark and mix well.
Stir milk mixture into eggs.
To assemble and bake:
Grate cheese (or use pre-grated). Sprinkle 1-1/2 cups into the egg mixture. Reserve 1/2 cup to sprinkle on top.
Transfer vegetables to egg mixture in baking dish. Spread out vegetables evenly.
Sprinkle remaining cheese on top. Dust with a little ground nutmeg, if desired.
Bake 35 minutes, or until firm and lightly browned. Let stand about 10 minutes before cutting into 4 squares (or 6 rectangles).