Heat 3 cups water until boiling and pour over the sun-dried tomatoes.
Allow the sun-dried tomatoes to steep for 15 minutes until soft.
Drain the liquid into a small bowl and set it and the sliced sun-dried tomatoes aside.
Heat 3 cups of water to the shiver stage in a shallow, medium-sized saucepan.
Add the asparagus and blanch for 4 minutes.
Place the cooked asparagus in ice water for 10 minutes.
Remove the asparagus from the water and cut the asparagus in 2-inch segments. Set them aside to dry on a paper towel.
Place the olive oil in a large skillet over medium-high heat.
Add the onions to the skillet and cook over medium heat until they begin to soften and turn slightly brown (about 7 – 10 minutes).
Reduce the heat to low, add the vodka, and cook for two minutes. Stir frequently.
Add the sun-dried tomato broth, the sun-dried tomatoes, canned tomatoes, and salt.
Simmer for 40 minutes, stirring occasionally.
When the sauce is almost cooked, place the 4 quarts of water in a large pot.
Add the linguine and cook about 15 minutes until just done (the pasta should have a slightly firm texture)
While the linguine is cooking, add the shrimp and the milk to the gently simmering sauce. Stir occasionally.
After about 10 minutes, add the asparagus to the sauce and fold in gently.
Drain the linguine. Add the pasta to the tomato/shrimp sauce and toss to coat the pasta with the sauce. Season to taste with fresh ground black pepper.
Served topped with the fresh basil.