Place a medium saucepan over medium heat, add 3 tablespoons of butter and allow to melt. Add the shallot and garlic and sauté until the shallot is soft and translucent, about 4 minutes.
Add the flour and cook, whisking until pale golden brown, about 30 seconds.
Stir in the tomato paste followed by the milk, whisking until completely combined. Lower heat to medium-low and let simmer, whisking occasionally, until the sauce has thickened, about 10 minutes.
Stir in the sun dried tomatoes. Remove from heat then cover and set aside.
Bring a large pot of salted water to a boil. Add the fettuccine and cook, stirring occasionally, until al dente, about 10 minutes. Reserve 1 cup of the pasta cooking water then drain and return the pasta to the pot.
In a large sauté pan over medium heat, add 2 tablespoons of the olive oil and heat through. Add 2 tablespoons of the butter and allow to melt. Add the shrimp and sauté on both sides until pink and no longer translucent, about 1½ minutes per side. Remove the shrimp from the pan and set aside on a plate.
Return the pan to heat, add the remaining olive oil and heat through. Add the remaining butter and allow to melt. Working in batches, add the mushrooms to the pan and sauté, stirring occasionally, until the mushrooms reduce in size as not to overcrowd the pan. Continue to cook until all mushrooms have been added and they are golden brown, about 5 to 6 minutes.
Add the sauce and mushroom mixture to the cooked pasta and toss until thoroughly coated in the sauce. Add ¼ cup of the pasta cooking water, tossing to combine. Add more pasta cooking water if needed. Stir in half of the parsley.
Divide the pasta among warmed pasta bowls and top with shrimp. Garnish with parsley and serve.