Boil the fettuccine
Bring a large pan of well-salted water to a strong boil. Add the fettuccine and cook until al dente, using the shorter timing for fresh pasta and the longer timing for dried.
Reserve the pasta water
Before draining, scoop out about 1 cup of the hot starchy cooking water. Drain the pasta well.
Melt the butter
Set a large wide saucepan or skillet over low heat and melt the softened butter gently. Once melted, remove the pan from the heat.
Coat the pasta
Add the drained hot fettuccine to the melted butter. Scatter over a handful of grated Parmigiano-Reggiano and add about 1/4 cup of the reserved pasta water.
Emulsify the sauce
Toss vigorously with tongs, adding the remaining cheese a little at a time and splashing in small amounts of pasta water as needed. Keep tossing until the butter, cheese and water form a smooth glossy sauce that clings to the pasta.
Serve immediately
Divide the fettuccine between warm bowls and finish with a little extra grated Parmigiano-Reggiano if liked.