Cut the corn cobs into 2-inch chunks.
In a large pot, heat the chicken stock until it begins to simmer. Add the corn cobs, cover and simmer for 10 minutes.
While the cobs are cooking, prepare a roux. Melt 2 Tbsp. of butter in a small sauce pan. When the butter is melted, whisk in the flour and cook, stirring constantly for one minute. Remove from heat and set aside.
Strain the chicken stock mixture into a bowl and discard the cobs.
Return the pot to the stove and add the remaining 1 Tbsp. of butter. When the butter is melted and sizzling, add the onion, bell pepper and fennel. Cook, stirring occasionally, until the onions are soft, about 3 minutes. Season generously with salt and pepper.
Whisk the roux mixture into the onion mixture, then add the potatoes, corn, 1 cup of the reserved chicken stock, and 3 cups whole milk. Bring the chowder to a boil, then reduce heat and simmer until the potatoes are tender, about 10 minutes.
Taste the chowder and adjust the seasoning as needed.
Just before serving, stir in the crab (reserving a few nice pieces for garnishing), sliced basil, and fennel fronds.
Garnish with a few additional pieces of crab meat and serve immediately.