Add olive oil to heated deep heavy skillet.
Add squash, garlic, half of salt and half of pepper to skillet and saute squash on medium high until it begins to color, approximately 7-10 minutes.
Add chicken stock and simmer until squash is thoroughly tender, approximately 7 minutes.Add rosemary and remaining salt and pepper to taste.
Puree sauce with immersion blender or in stand blender until smooth. Note: if you prefer a more rustic texture, remove some squash before pureeing and cut into smaller cubes and add back to puree.
In the meantime, cook pasta per package directions in boiling salted water until al dente. Drain but do not rinse.
Heat olive oil in second heavy skillet over medium high heat.
Add shrimp and saute until pink about 3-4 minutes. Do not overcook.
In large pot, combine cooked pasta, sauce, and 1/2 of milk and stir until combined. Simmer over low heat, stirring occasionally. Add rest of milk slowly to reach desired consistency. Simmer until heated through.
Serve pasta in individual bowls with shrimp placed on top.
Sprinkle Parmesan on dish and serve hot.