Preheat your oven to 400°F. While it heats, prepare your mise en place: halve the cherry tomatoes, crumble the feta cheese into bite-sized pieces, mince the garlic cloves, and cut the salmon into 4-6 equal portions. Tear the basil roughly and set aside separately—we'll add it after baking to preserve its fresh flavor. Having everything prepped and ready will make assembly seamless once the oven is hot.
In a large baking dish or similar size (roughly 9x13 inches), arrange the salmon portions, halved tomatoes, and crumbled feta. Drizzle with the extra virgin olive oil, then sprinkle with sea salt, black pepper, and red pepper flakes. The oil will help create a rich sauce as everything bakes together. I like to distribute the feta pieces evenly so each bite of salmon gets a bit of cheesy richness.
Place the baking dish in the preheated 400°F oven and bake for 40-45 minutes, until the salmon is cooked through and flakes easily with a fork, and the tomatoes have softened and begun to break down. The feta will soften and mingle with the tomato juices to form the base of your sauce. While this bakes, move to Step 4 to cook your pasta.
As the salmon bakes, bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente. Before draining, reserve 1/2 cup of the starchy pasta water—this will help emulsify and adjust the consistency of your final sauce. The timing should work out so the pasta finishes right around when the salmon comes out of the oven.
Remove the baking dish from the oven and add the minced garlic and torn basil, stirring gently. Using a fork, break apart the softened feta and mash the cooked tomatoes to create a chunky, creamy sauce. Flake the cooked salmon into bite-sized pieces right in the pan, being careful not to break it apart too much. Add the cooked pasta to the baking dish and toss everything together gently. If the sauce seems too thick, add reserved pasta water a little at a time until you reach your desired consistency. I find starting with a quarter cup and tasting as you go gives you better control than dumping it all in at once.