Preheat oven to 400 degrees.
In a large, deep braising pan, add the block of feta cheese to the center. Arrange the salmon in a single layer in the pan and add the spinach on top.
Toss in the tomatoes around the pan, followed by garlic, pesto, Calabrian chiles, and seasonings. Cover with the lid and place in the oven for 25 minutes.
While the salmon bakes, bring a large pot of water to a boil and cook the pasta to al dente according to package instructions. Reserve ½ cup of pasta water before draining.
Remove the pan from the oven. Use a large fork to break up some of the tomatoes (leaving some whole) and mash the feta cheese, mixing it into the crushed tomatoes. Flake the salmon into chunks.
Add the drained pasta to the pan with the other ingredients. Toss until evenly incorporated with the toppings and pan sauce, adding a little reserved pasta water if needed to loosen the sauce.
Squeeze the lemon juice over the pasta. Add the parmesan cheese and toss to combine. Top with fresh basil before serving.