1 1/2 pounds (31 to 35 per lb.) shrimp, shelled (shells reserved), deveined, and cut into 1/2-in. pieces
About 3 cups reduced-sodium chicken broth
1 cup dry white wine
1 medium onion, peeled and quartered
4 garlic cloves, halved lengthwise
3 celery stalks, cut into chunks
1 medium carrot, cut into chunks
3 oregano sprigs
2 thyme sprigs, plus fresh thyme leaves for garnish
1/2 teaspoon black peppercorns
3/4 cup butter
1/2 cup flour
1 tablespoon paprika
1/4 teaspoon cayenne
2 cups half-and-half
1 1/2 teaspoons kosher salt
How to Make It
In a large saucepan, combine shrimp shells, 3 cups broth, the wine, onion, garlic, celery, carrot, oregano and thyme sprigs, and peppercorns. Bring to a boil, then simmer, covered, 30 minutes. Strain into a large glass measuring cup; if you have less than 3 1/2 cups, add more broth.
Melt butter in same pan over medium heat. Stir in flour, paprika, and cayenne and cook, stirring often, until mixture just starts to darken and smell nutty, about 3 minutes. Whisk in broth mixture and half-and-half, increase heat, and continue whisking until mixture boils and thickens, about 8 minutes. If bisque is too thick, add a little more broth. Stir in salt and shrimp, remove from heat, and let sit until shrimp pieces are pink on the outside and opaque but still moist-looking inside (cut to test), about 3 minutes.
Ladle bisque into shooter glasses or small cups and sprinkle thyme leaves on top.