Heat the olive oil in a large skillet over medium heat. If possible, use a skillet wide enough to fit the fettuccine flat.
Add the minced garlic and chopped shallot with a small sprinkle of salt. Cook for about 2 minutes, stirring occasionally, until the garlic is softened and the shallot turns translucent. Do not let it brown.
Pour in the vegetable broth and non dairy milk. Add the salt and stir. Place the dry fettuccine into the pan and gently press it down so it is mostly submerged in the liquid. As it softens, continue pressing it down so it fits fully in the pan.
Bring the mixture to a boil, then reduce to a gentle simmer. Stir occasionally and separate any noodles that start sticking together. Cook for about 20 minutes, or until the pasta is tender and the sauce has thickened around it.
If too much liquid cooks off before the pasta is done, lower the heat and add a splash more non dairy milk.
Taste and adjust seasoning with salt, black pepper, dried oregano, or red pepper flakes. Serve immediately with chopped fresh basil or parsley on top.