Cut the kernels from the corn cobs and set the kernels aside. Place the bare cobs and stock in a medium saucepan. Bring to a gentle simmer, cover, and cook for 15 minutes. Remove the cobs, allowing the liquid to drip back into the pan. Measure the stock and add enough water to bring it back to 3 cups.
Melt the butter in a Dutch oven over medium heat. Add the onion, celery, and bell pepper. Cook for 7–8 minutes, stirring occasionally, until the vegetables soften without browning. Add the garlic and cook for 30 seconds.
Sprinkle the flour over the vegetables. Stir continuously for 2–3 minutes to cook off the raw flour taste, keeping the mixture pale. Stir in the Cajun seasoning and salt. Slowly pour in the warm corn stock, whisking as you go until the mixture is smooth. Add the corn kernels. Bring the bisque to a gentle simmer and cook uncovered for 12–15 minutes, stirring occasionally, until the corn is tender and the broth has thickened slightly.
Transfer about 2 cups of the soup to a countertop blender and blend until smooth, then stir it back into the pot. Alternatively, use an immersion blender for a few short pulses directly in the pot. Leave plenty of corn kernels whole. If using a countertop blender, vent the lid and blend hot soup carefully.
Reduce the heat to low and stir in the half-and-half. Add the crabmeat, green onions, and parsley. Heat gently for 2–3 minutes, stirring carefully to keep the crab pieces intact. Do not let the bisque boil.
Stir in 1 tsp lemon juice. Taste and add more lemon juice or salt as needed. Ladle into bowls and serve warm, with a little extra parsley or green onion on top if desired.
