Cook the spaghetti or linguine according to package instructions in a large pot of salted boiling water until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Stir in the Calabrian chili paste and cook for an additional 30 seconds.
Add the drained diced tomatoes and dried oregano to the skillet. Season with salt and pepper, and let the mixture simmer for about 5 minutes, allowing the flavors to meld.
Add the cooked pasta to the skillet, tossing to combine. If the pasta seems dry, add some reserved pasta water a little at a time until you reach the desired consistency.
Remove from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve immediately, garnished with fresh basil leaves and additional Parmesan if desired.