Bring a large pot of generously salted water to a boil. Cook the pasta until al dente. Before draining, reserve 1 cup of the pasta water.
While the pasta cooks, combine the parsley, oregano, garlic, vinegar, olive oil, red pepper flakes, and salt in a food processor. Pulse until finely chopped but not fully smooth.
Pat the tilapia fillets dry and season with salt and pepper. Heat the olive oil in a skillet over medium-high heat and sear for 3 to 4 minutes per side.
Set 2 tablespoons of the chimichurri aside for garnish. Whisk the cream into the rest, off the heat, until smooth.
Toss the hot, drained pasta with the creamy chimichurri over the lowest possible heat, adding splashes of the reserved pasta water until silky.
Flake the seared tilapia over the pasta, drizzle with the reserved plain chimichurri, and serve immediately.