Although the meaning of the word bisque has evolved over time, it has always referred to a thick soup of one kind or another.
For a long time, however, the word bisque had a very specific meaning: a particular type of soup made from crustaceans — lobster, crab, shrimp and crayfish — and thickened with rice.
In the more distant past, the word encompassed soups made from quail or pigeon, sometimes with chunks of crayfish meat added.
And you can't blame restaurateurs for wanting their soups to be bisques. It's a beautiful word, for one thing. But also, crucially, you can charge a lot more for a soup if you call it a bisque.
Not that that's fraud or anything. But using the word bisque to describe a puréed pumpkin soup, for example, ends up turning the word bisque into just another word for soup. Again, there's nothing intrinsically wrong with that. But if that's the case, we're still going to need a word to describe the kind of bisque made from lobster, crab, et al., because that's the characteristic that makes it unique.
To be clear, it's not merely the choice of ingredient that makes bisque unique, it's also the technique for utilizing that ingredient, including the parts you can't eat.
Bisque Gets Its Flavor from Roasted Shells
The shells of crustaceans happen to be loaded with flavor. But since you can't eat them, you have to find a way to extract that flavor, namely by roasting and then simmering them.
So, to make a lobster bisque, you'll begin by steaming a live lobster. Be sure to save the liquid you used to steam it.
After removing the cooked meat from the lobster, drizzle the shells with olive oil and roast them in a hot oven along with some aromatics like onions, carrots, maybe some lovely fennel, until everything is a gorgeously brown and toasty.
Deglaze your roasting pan with something decadent like brandy or cognac, reduce, then pour back the steaming liquid and simmer with a couple of bay leaves until it's reduced quite a lot. This will concentrate and intensify the flavor even further.
Strain and use the resulting stock as the base for your bisque. Traditionally bisque is thickened with rice and then puréed along with some or all of the meat. Puréeing the meat heightens the flavor of the bisque and also helps with thickening. You could purée half the meat and reserve some fat chunks of tail and claw meat to add in at the end.
Here's a medium-difficulty lobster bisque recipe.