Parboil sausages in a skillet with a few inches of water to cook through.
Meanwhile, heat EVOO, a couple of turns of the pan, in a large skillet over medium heat. Add fennel, onions, garlic, thyme, salt and pepper. Cook until very soft and tender, 15 minutes. Deglaze with Pernod or St. Germain then the white wine. Reduce at a low simmer a few minutes more.
Heat a griddle or cast-iron pan over medium-high heat with a drizzle of oil to coat.
Split the sausages lengthwise but do not cut through. Brown on both sides in the hot pan. Place sausages in sub rolls and top with fennel and onions, and shaved Parmigiano cheese. Garnish with basil or tarragon, chopped fennel fronds and some parsley.