Cook the spaghetti according to package directions.
Place the remaining ingredients in a high-speed blender. Blend on high until completely smooth.
Drain the spaghetti, reserving the pasta water. Return the spaghetti to the saucepan and add the carbonara sauce. Add just enough so that the sauce coats the pasta. Add a small amount of pasta water if the sauce feels too thick.
Plate the spaghetti. Top each serving with a generous amount of freshly ground black pepper and either sun-dried tomatoes or vegan bacon.