Start by getting all your ingredients prepped. Cut the fennel into 1-inch pieces, measure out your wine, smash or chop the olives, and have all the ingredients ready to cook.
Heat a large fry or sauté pan over medium heat until a drop of water evaporates immediately when hitting the pan's surface. Add two tablespoons of oil and then the sausages. Add the sausages to the pan and cook for about 5 minutes, being sure to turn so they don't burn.
When the sausages are brown on all sides, add the wine and bring to a boil. Cook until the wine is reduced by half. Transfer the sausages to a plate and pour the remaining wine over them—reserve for later.
Add the remaining two tablespoons of olive oil to the pan and then the garlic. Cook for about a minute until the garlic begins to sizzle. If you use the peperoncino flakes, now's the time to add them. Now it's time to add the smashed olives and cook for a minute or two.
Toss in the chopped fennel and combine with the garlic and olives. Season with a bit of salt, cover the pan and cook over medium heat for about 20 minutes until the fennel softens and starts to turn golden. Be sure to stir the ingredients every once in a while so they don't burn.
Lidia suggests adding a little water to the pan if the fennel is still hard after 20 minutes. I didn't find this to be the case.
When the fennel is ready, add the sausages to the pan, the wine, and any accumulated juices. Mix everything to combine flavors and cook uncovered until the fennel caramelizes. This should take about 5 minutes.
Taste and adjust the seasoning with salt and pepper to taste.
Serve alone or with pasta, rice, couscous, or orzo as we did.