Preheat your oven to 350°F / 175°C.
Drain the marinated artichoke hearts, reserving ¼ cup of the oil from the jar.
Heat this reserved oil in a large, 10-inch oven-safe skillet or casserole dish over medium heat.
Add the chopped onion and sauté until softened and just beginning to turn golden, about 5-7 minutes.
While the onions cook, thickly slice or quarter the drained artichoke hearts.
In a separate medium bowl, whisk the eggs, salt, a generous amount of fresh-ground black pepper, and flour until the mixture is completely smooth and free of lumps.
Stir the grated Cheddar and Parmesan cheeses into the egg mixture.
Add the chopped artichoke hearts to the skillet with the sautéed onions and stir to combine.
Spread the artichoke and onion mixture evenly across the bottom of the skillet.
Pour the egg and cheese mixture evenly over the vegetables. Use a spatula to gently spread it to the edges, ensuring everything is covered.
Bake for 20 to 25 minutes, or until the puff is set in the center, golden brown, and slightly crusty on top.
Let it cool for at least 10 minutes before slicing and serving.
Let the puff rest for at least 10 minutes after baking. This allows it to set properly, making it much easier to slice into clean wedges or squares.
