Prepare each flower by snipping off its stem and the pointy bits of the sepal. If not using Hannahbells, which seem engineered for this purpose, cut cheese into pieces about the size of the last inch of your pinkie, one for each flower. Gingerly hide a cheese bit inside of each flower, and give the petals a gentle but firm twist to enclose it.
Find two broad dishes, like pie plates. Stir together the sifted cornmeal, flour, and salt and pepper to taste in one and beat the egg in the other. Run each flower through the dry mixture, then the egg, and then back through the dry mixture again. Set aside the breaded flowers on a dry surface.
Heat a ¾-inch depth of olive oil in a heavy-bottomed skillet over medium-high heat. When it smells fragrant (but before it smokes) place the flowers in the skillet, and adjust the flame so that they sizzle in a moderate way. Cook golden brown and crisp on all sides.
Serve at once on a bed of tasty greens or with just a sprinkle of salt.