Preparation

Make the pistou:

• Put the garlic, basil, and a pinch of sea salt in a mortar and pound until puréed smoothly. (Alternatively, use a chef’s knife to chop the basil very finely and to mash the garlic to a paste with the salt; then combine them in a small bowl.) Add 2 Tbs. of the olive oil, mix, and let infuse at room temperature for 1 hour.

Grill the corn:

• Heat a gas grill to high or prepare a hot charcoal fire. Cut off the tip of the corn’s husks (to make it easier to remove the husks once grilled). Grill the corn in the husk for 15 to 20 minutes, giving it a quarter turn every 5 minutes, keeping the grill covered (the kernels should be cooked but not charred). When it’s cool enough to handle, remove all of the husk and silk. With a sharp knife, cut the kernels off the cob. Set the kernels aside.

Make the soup:

• Core the tomatoes and cut them into chunks. Working in two batches, put half the tomatoes in a blender with 1 tablespoon of the lemon juice and 1/4 cup of the olive oil in each batch. Season with a generous pinch of sea salt and black pepper, and blend on high speed until smooth. Strain through a fine sieve, pressing on the solids to force the liquid through the mesh. Taste and adjust the seasonings if needed. Refrigerate until serving time.
• Pick through the crabmeat for any bits of shell. Put it in a bowl along with 1 Tbs. lemon juice, 1 Tbs. olive oil, 1 tsp. sea salt, and black pepper totaste. Add the grilled corn kernels; mix thoroughly. Adjust the seasonings if needed.
• Divide the soup among four chilled soup bowls. Spoon a mound of crab salad in the center of each serving. Stir the pistou and then drizzle it over the soup and crab. Serve at once.