If you live in an area such as Florida, where mullet are harvested privately and commercially, you will have the option of purchasing white or yellow roe during the mullet's spawning season. The white roe is not roe at all but milt, the male equivalent. It's also a delicacy, but is less rich than the yellow or true roe. Mullet roe consists of thousands of fine eggs contained in an oblong membrane, rather like a sausage in its casing. There are many ways to cook it, but pan-frying is traditional.
Rinse the lobes of roe carefully under cold running water, taking care not to break the membranes.
Heat about an inch of lightly salted water in a skillet until it's at a moderate simmer, with just an occasional bubble rising to the surface. Pierce each roe in three or four places with the tip of a toothpick, so it doesn't burst, and slide it carefully into the water. Poach for four or five minutes until the roes have firmed, then remove them carefully with a slotted spoon.
Dry the roes by rolling them carefully on a mat of clean paper towels. Season the roes with salt and pepper, then dredge them in flour and brush off the excess.
Heat a heavy-bottomed skillet, and pour in approximately a tablespoon of vegetable oil. Transfer the floured roes to the skillet, taking care not to crowd them. Fry them in two batches, or two skillets, if need be.
Cook the roes until they are golden brown, approximately three to five minutes on each side. Keep a lid or spatter screen on the pan, in case one of the roes bursts and sends a spray of oil and scalding-hot eggs across the stove.
Serve hot, allowing one or two roes per person, depending whether mullet roe is the entire entree.
Once poached, the roes can be cut into portions using a sharp knife and finished in a cream sauce or wine-based sauce, then served alongside rice or over pasta.
The Greeks make a dip called taramasalata from mullet roe. The Italians salt it and dry it to make bottarga, a sort of intensely flavorful fish-egg jerky. It's grated or thinly sliced over foods as a garnish or accent.
Most recipes for mullet roe and shad roe are interchangeable, though shad roes are larger. If you are too far north for mullet in the autumn, you should be able to find shad roe in the spring.