Thick, creamy chowders brimming with seafood, potatoes, and corn are the pride of lunch spots throughout the Northeast. This one has rich flavor and comes together fast.
In a medium pot, melt butter over medium. Add onion and saute until translucent, about 6 minutes. Stir in corn kernels and potatoes; season with salt and pepper. Add milk, 1 cup water, and corncobs.
Increase heat to medium-high and bring to a boil, then reduce to a simmer and cook until potatoes are tender when pierced with a knife, about 8 minutes. Add shrimp and cook until opaque throughout, 3 to 5 minutes. Discard cobs and stir in basil.
Divide among bowls and top with more basil. Serve with bread if desired.
To store, refrigerate in an airtight container, up to 3 days.