Sprinkle the shrimp with a scant 1/4 teaspoon salt and a few generous grinds of black pepper. Put a 12-inch skillet (not nonstick) over medium-high heat for 1-1/2 minutes. Add 2 tablespoons of the oil and once it's shimmering hot, add the shrimp in a single layer. Cook undisturbed until the shrimp browns nicely, about 2 minutes. Flip the shrimp and brown the second side, about 1-1/2 minutes. Transfer to a large plate. The shrimp should still be a little undercooked.

Reduce the heat to medium. Add the remaining 2 tablespoons oil and the fennel and garlic. Sprinkle with 1/2 teaspoon salt and cook, tossing often, until the fennel is very soft and golden brown in places, 6 to 8 minutes.

Carefully add the Pernod (it may flame up) and cook, stirring, until any flames die out and the Pernod has almost evaporated, about 1 minute. Add the tomatoes and their juice, the thyme, and about half the parsley. Bring to a boil and then reduce the heat to a gentle simmer and cook for 3 minutes to meld the flavors. Add the shrimp, and cook, tossing, until it's opaque throughout (cut one in half to check), 1 to 2 minutes. Season to taste with salt and pepper. Serve immediately, sprinkled with the remaining parsley.