Pour olive oil into a 5- to 6-quart pan over medium-high heat. When hot, add onion and garlic and stir often until limp, 3 to 4 minutes. Add broth, wine, tomato paste, basil, oregano, and thyme; stir often until boiling. Reduce heat and simmer, stirring occasionally, to blend flavors, about 10 minutes. Add salt and pepper to taste.
Add crabs and simmer, occasionally stirring gently, until hot, about 5 minutes.
Ladle crabs and broth mixture into wide bowls and garnish with basil sprigs.
How to cook crab
Keep live crabs loosely covered in the refrigerator up to 12 hours. Grasp crabs carefully from the rear end, between the legs, and put in a pan to make sure they fit, with 3 to 4 inches of clearance below pan rim. Remove crabs and fill pan with enough water to cover crabs by 2 to 3 inches. Cover pan and bring water to a boil over high heat.
One at a time, grasp crabs as described above and plunge them headfirst into the boiling water; if you have too much water, ladle out excess and discard. Cover pan and start timing. When water resumes boiling, reduce heat to a simmer. Cook 1 1/2- to 2 1/2-pound crabs 15 minutes, 3-pound crabs about 20 minutes.
Drain crabs; to be able to handle quickly, rinse briefly with cool water.
How to clean, crack, and shell crab
Pull off and discard triangular flap from belly side.
Turn crab belly side down; pulling from the rear end, lift off back shell. Drain and discard liquid from shell. If desired, scoop soft, golden crab butter and white crab fat from shell into a small bowl to eat by the spoonful with crab or to stir into a dipping sauce. If using back shell for garnish, break bony section (mouth) from front end of shell and discard. Rinse shell well and drain.
On the body section, pull off and discard reddish membrane that covers the center (if it hasn't come off with the back) and any loose pieces. Scoop out any remaining golden butter and add to bowl. Pull off and discard long, spongy gills from sides of body. Rinse body well with cool water.
Twist legs and claws from body. Using a nutcracker or wood mallet, crack the shell of each leg and claw section. With a knife, cut the body into quarters.
Break apart legs and claws; using your fingers, a small fork, a pick, or a crab leg tip, remove meat. Pull body sections apart and dig out pockets of meat. Discard shells. One cooked, cleaned 1 3/4- to 2-pound crab (with back shell) yields 7 1/2 to 8 ounces (1 1/3 to 1 1/2 cups) of meat; heavier crabs do not always have more meat.