Bring a big pot of salted water to a boil. Add spaghetti and cook until just shy of al dente — about 1 minute less than the box says. We're finishing it in the sauce, so don't fully cook it yet.
While pasta cooks, heat olive oil in a large skillet over medium-high heat. Add minced garlic and let it sizzle for about 30 seconds until fragrant. Don't let it brown or it'll taste bitter.
Add sliced chicken breast to the skillet and cook for 3-4 minutes until the outside turns white. Stir it around so it cooks evenly. Mine always sticks a little to the pan and that's fine.
Toss in the cherry tomatoes and red pepper flakes, then give everything a good stir. You'll hear it sizzle immediately. Add the chicken broth and oregano, then let it bubble away for about 2 minutes.
Here's where the magic happens — the tomatoes start bursting open and releasing all their juice. If a few haven't popped yet, gently press them with your spoon. The sauce should look a little watery at this point.
Add the drained pasta straight into the skillet with the burst cherry tomato pasta family sauce. Toss everything together for about 1-2 minutes so the pasta absorbs the liquid. Taste and adjust salt as needed.
Turn off the heat and stir in the butter and shredded mozzarella. Don't panic if it looks a little separated — keep stirring and it'll come together into a creamy coating. It thickens up fast.
Scatter fresh basil on top and serve immediately while everything's still warm and creamy.