For the aspic
2 1/2 pounds ripe heirloom tomatoes (about 4 beefsteak)
About 2 1/2 tablespoons (3 envelopes) unflavored gelatin
1/4 cup very hot water
2 teaspoons balsamic vinegar
1 1/2 teaspoons kosher salt
1 teaspoon chopped thyme leaves
1/4 teaspoon crushed red pepper flakes
For the salad
One 3-pound rotisserie chicken
28 ounces canned, no-salt-added cannellini beans, rinsed and drained
1 small bulb fennel, quartered, cored and very thinly sliced (about 1 1/2 cups)
6 tablespoons extra-virgin olive oil, plus more for drizzling
1/4 cup red wine vinegar
2 tablespoons fresh lemon juice
3 ounces baby arugula (about 4 cups)
3/4 cup Parmigiano-Reggiano shavings (made using a peeler), plus more for garnish
12 leaves basil, torn, plus more for garnish
Kosher salt
Freshly ground black pepper
For the aspic: Lightly grease eight 4-ounce ramekins with cooking oil spray.
Seed one of the tomatoes, letting the seeds, gel and liquid fall into the bowl of the food processor. Finely dice the flesh to yield 1/2 cup; transfer to a small bowl. Cut the remainder of the seeded tomato and the remaining whole tomatoes into 1-inch chunks and add to the food processor. Process until completely pureed, about 1 minute. Strain into a 1-quart liquid measuring cup through a fine-mesh strainer, using a flexible spatula to press through as much of the juice as possible; discard any solids in the strainer. You’ll need 23/4 cups of juice; reserve any extra for another use (such as a gazpacho or vinaigrette). If you don’t have enough juice, add water to yield a total of 2 3/4 cups.
Transfer a generous 1/2 cup of the juice to a very wide, shallow bowl. (You need a large surface area.) Sprinkle the gelatin evenly onto the juice, letting it sit on the surface. After 10 minutes, add the hottest possible tap water and stir until the gelatin has dissolved and the mixture is thick yet not lumpy. Add it to the remaining 2 1/4 cups of tomato juice in the measuring cup, stirring to incorporate completely. Add the reserved 1/2 cup of diced tomato, along with the vinegar, salt, thyme and crushed red pepper flakes.
Pour equal amounts of the aspic mixture into each ramekin. Cover with plastic wrap and refrigerate until the aspic sets, at least 4 hours and up to 2 days.
For the salad: Discard the skin, bones and all visible fat from the chicken. Cut the remaining meat into 1/2-inch pieces, placing them in a large serving bowl as you work. The yield is about 6 cups.Add the beans, fennel, oil, vinegar and lemon juice, and toss well to incorporate. Let the salad sit for 5 minutes, so the fennel begins to soften and the chicken picks up the flavor of the dressing. Add the arugula, Parmigiano-Reggiano and basil, and toss well. Taste, and add salt and pepper as needed.