Bring a large pot of generously salted water to a boil. Cook the gluten free fettuccine according to package directions until just al dente. Before draining, reserve 1 cup of the starchy pasta water.
While the pasta cooks, whisk together the egg yolks, whole egg, pecorino romano, parmesan, and black pepper in a medium bowl until smooth and creamy. Set aside.
Heat the olive oil in a large deep skillet over medium heat. Add the diced pancetta and cook for 5 to 7 minutes, stirring occasionally, until golden and crispy.
Add the smashed garlic cloves to the skillet and cook for 1 minute until fragrant. Remove and discard the garlic.
Remove the skillet from the heat and add the drained pasta directly to the pancetta. Toss well to coat in the rendered fat.
With the skillet still off the heat, pour the egg and cheese mixture over the pasta. Toss vigorously and continuously, adding reserved pasta water a couple of tablespoons at a time, until a silky and creamy sauce forms that clings to every strand.
Serve immediately with an extra generous grinding of black pepper and more grated pecorino on top.