Feeds 2-4 people, depending on appetite and what else is on the table.
Not yet test-made, what the trial has to prove: (1) whether 2 cups of water is the right amount for homemade gluten-free fettuccine; GF pasta sheds more starch than wheat pasta, so the sauce may set thicker (the hot-water splash in the method is the fix), or the strands may need a little more water to finish cooking; (2) whether the strands hold together through the skillet toss without breaking up; be gentle with the tongs, and lift-and-turn rather than stir.
No cream, no flour, no garlic. The traditional Alfredo is pasta, butter, cheese, water, and salt, and the starch in the cooking water does the thickening.
Grate the cheese yourself, as fine as you can. Pre-grated cheese is coated to keep it from clumping in the bag, and that coating keeps it from melting smoothly into an emulsion.
Grana Padano is the pick for the skillet version because it is aged less than Parmigiano-Reggiano and melts more smoothly; Parmigiano-Reggiano works in its place.
Rennet note: Grana Padano and Parmigiano-Reggiano are traditionally made with animal rennet. If the meal needs to be fully vegetarian, use a hard Italian-style grating cheese made with vegetarian rennet and grate it the same way.
Leftovers: this dish is at its best the minute it is made. The emulsion tightens as it sits; revive leftovers gently over low heat with a splash of water, tossing until glossy again.