Combine bok choy and salt in a bowl and rub leaves with salt.

Melt 1 1/2 ounces butter in a pot over medium heat. Add bacon and garlic and cook until garlic has softened and bacon is crisp, about 3 minutes. Add bok choy, cover pot, and cook until leaves have softened, about 3 minutes. Add water, cover, and simmer for 20 minutes. Season with basil and remaining butter.

Meanwhile, fill a large pot with lightly salted water and bring to a rolling boil. Cook fettuccine at a boil until tender yet firm to the bite, about 8 minutes. Drain and keep warm.

Drain half the liquid from the pot with the bok choy and transfer remaining contents to a skillet over medium-high heat. Season with pepper and add milk. Mix in cooked fettuccine. Cook and stir for 1 minute.