In a large skillet, melt the lard over low heat. Add the thinly sliced onions and cook gently until softened and translucent. Splash in the white wine and allow the alcohol to evaporate.
Pour in the vegetable broth. Sprinkle the flour over the onions, season with salt and pepper, and stir thoroughly. Cover with a lid and simmer over low heat for about 1 hour.
Remove the skillet from the heat. In a small bowl, beat the eggs together with the Pecorino Romano, then stir this mixture into the cooked onions.
Butter a baking dish and pour in the onion mixture. Bake in a preheated oven at 180°C (350°F) until the top is set and golden brown.
Remove the cipollata from the oven and serve warm.