I start by cooking the fettuccine in a large pot of well-salted boiling water, following the package directions until it's al dente. Right before draining, I scoop out a full cup of the starchy pasta water and set it aside, since I'll need it later to loosen the sauce. Then I drain the noodles and let them sit in the colander until I'm ready for them.
While the pasta cooks, I rinse my broccoli florets and pat them fairly dry. In a large skillet, I heat one tablespoon of olive oil over medium-high heat, add the broccoli, and season it with salt and pepper. After about three minutes of sautéing, I pour in the quarter cup of water and let the florets steam for another four minutes before transferring them to a plate.
Using that same skillet, I add the rest of the olive oil and toss in my bite-sized chicken pieces, seasoning them well. I let the chicken cook for four to five minutes, stirring occasionally, until every piece is golden and cooked through. Once it's done, I move the chicken onto the same plate as my broccoli so both are ready to go.
In the empty skillet, I melt the butter and pour in the heavy cream along with the garlic powder and a pinch of nutmeg, scraping up any browned bits stuck to the pan for extra flavor. I bring this to a gentle simmer, then whisk in the freshly grated parmesan until it melts into a smooth, creamy sauce. This step only takes a couple of minutes over low heat.
By now my sauce is thick, so I whisk in that reserved cup of starchy pasta water a little at a time until the consistency feels silky rather than gluey. I taste it at this point and adjust the salt and pepper, keeping in mind the pasta water already carries some saltiness of its own.
Finally, I add the drained fettuccine, the cooked chicken, and the steamed broccoli back into the skillet with the sauce. I toss everything gently with tongs until each strand of pasta and every piece of chicken and broccoli is coated in that creamy sauce, then I serve it warm with extra parmesan on top.