Bring a large pot of salted water to a boil.
Meanwhile heat olive oil in a large skillet. Add prosciutto slices, side by side and let it crisp on both sides before removing from skillet (about 2-3 mins each side). Transfer to a paper towel to absorb the excess oil and set aside.
Now it’s time to put the pasta in pot with boiling water. Undercook the pasta by about 3 mins.
Add in shallots and mushrooms to the skillet, stir until mushrooms are browned.
Take about 3/4 cup of pasta water and dissolve the vegetable base in it. Add this vegetable base water to the skillet and stir. Add wine at this point.
Remove the pasta from pot and add to the skillet (no draining needed). Gently fold to combine with sauce and mushrooms. If needed add more pasta water to the skillet. Turn heat down, cover and let it simmer for up to 5 minutes.
Meanwhile chop up the prosciutto into bite size. Also remove tarragon leaves from stem.
Remove pasta from stove. Add in chopped up prosciutto and fresh tarragon. Serve hot.