Bring a large pot of generously salted water to a boil. Cook the pasta 1 minute less than the package says, usually 9 to 10 minutes, until it is firm to the bite. Reserve 1/2 cup (120ml) of the pasta water, then drain.
While the water heats, season the tilapia with the salt and pepper. Heat the olive oil in a large, deep skillet over medium-high heat until it shimmers.
Sear the fillets for 2 to 3 minutes per side, until golden on the outside and just opaque and flaking in the center, at 63°C (145°F). Move them to a plate. Do not wash the skillet.
Lower the heat to medium. Cook the shallot in the same skillet for 2 minutes, until soft and translucent. Add the garlic and tomato paste and stir for 1 minute, until the paste darkens to brick red and smells sweet.
Add the tomatoes, herbes de Provence, and stock. Scrape up the browned bits from the pan. Simmer for 8 minutes, stirring now and then, until the sauce thickens and the oil begins to shimmer at the edges.
Stir in the olives, capers, and cream. Simmer gently, not boiling hard, for 3 minutes, until the sauce turns a pale coral and coats the back of a spoon.
Add the drained pasta and toss for 1 minute so it finishes cooking in the sauce, adding a splash of the reserved pasta water if the sauce is too thick.
Take the skillet off the heat. Flake the tilapia into large pieces and fold it in gently with the lemon zest and juice. Scatter parsley over the top and serve right away.