Grill or boil your corn (for 6-7 minutes in salted water). Shave off the kernels from the stalks with a sharp knife. Reserve for later.
Shrimp:
Coat the shrimp in your olive oil and seasonings. Heat a large deep skillet on medium high and cook your shrimp for 1-2 minutes per side. Remove them from the pan promptly and cover to keep warm.
Assembly:
To the same pan, melt the butter. Sauté your shallot for a minute or two and then the garlic for 30 seconds. Add in the milk, broth and pasta and bring to boil. Reduce the heat to low and simmer cook your pasta until cooked al dente. Season with salt and pepper to taste. Stir occasionally and stay on top of it; it can and will stick.
Once pasta is cooked, stir in your grated parmesan and heavy cream for 1 minute. Remove the pan from the burner and mix in your corn. Taste and adjust seasonings if necessary. Plate your pasta and top with shrimp, chives garnish and more grated cheese (if you like).