Bring a large pot of salted water to a boil and add your fettuccine. Cook according to package directions until al dente (usually around 8-10 minutes). Don't overcook it or you'll end up with mushy pasta that falls apart when you toss it. Reserve 1/2 cup of pasta water before draining—this starchy liquid is your secret weapon for the sauce.
While the pasta cooks, grab a large skillet and heat the olive oil and butter together over medium heat. Once the butter starts foaming, you'll know it's ready to go. Don't crank the heat too high or the butter will brown and taste nutty (sometimes that's good, but not for this creamy garlic pasta recipe).
Add your minced garlic to the hot oil and butter, stirring constantly for about 30-45 seconds. You want to smell that amazing garlic aroma but not let it get dark brown. I always stand there and breathe it in—kitchen smells that good don't happen every night, right?
Pour in the chicken broth and bring everything to a gentle simmer. Add the dried thyme, black pepper, and salt, then let it bubble away for about 2 minutes. This step builds flavor in the background while the pasta finishes cooking.
Reduce the heat to low and slowly pour in the heavy cream, stirring as you go. It'll look super creamy and rich at this point, which is exactly what you want. Don't panic if it looks a little separated at first—keep stirring and it'll come together beautifully.
Add the cooked fettuccine directly to the cream sauce along with the frozen peas. Toss everything together for about 1-2 minutes until the peas are heated through and warmed all the way. If your sauce feels too thick, splash in some of that reserved pasta water until you get the consistency you like.
Remove from heat and finish with the Parmesan cheese and fresh parsley. Give it one final toss so everything's evenly coated. Taste and adjust the seasoning if needed—this is your dish, so make it perfect for your palate.