Make bell pepper layer: Feed bell pepper and red tomato through an electric juicer. Pour juice through a fine sieve into a small bowl; discard any solids. Skim foam from surface with a spoon. Stir in hot sauce, 1/4 teaspoon salt, and 1/2 teaspoon lemon juice. Sprinkle 1 envelope gelatin over top. Let stand 5 minutes.
Transfer mixture to a small saucepan. Cook over medium heat, stirring constantly, until gelatin has just dissolved, about 1 1/2 minutes. Let cool slightly. Transfer bell pepper mixture to a 4-cup scalloped gelatin mold. Refrigerate until just set and still sticky, about 20 minutes.
Make gazpacho layer: Process yellow tomato flesh, the cucumber, and scallions in a food processor until almost pureed, about 10 seconds. Transfer vegetable mixture to a large bowl. Finely chop basil; add basil, 1 teaspoon each salt and lemon juice, and the vinegar to bowl; season with salt and pepper. Set aside.
Puree reserved yellow tomato seeds and pulp with the garlic in a food processor. Pour through a very fine sieve into a medium bowl; discard solids.
Sprinkle remaining gelatin over garlic mixture. Let stand 5 minutes. Transfer to a saucepan. Cook over medium heat, stirring constantly, until gelatin has dissolved, about 2 minutes. Stir garlic mixture into the reserved gazpacho.
When bell pepper layer has just set, pour gazpacho layer on top. Refrigerate until set, about 4 hours. Aspic can be refrigerated, loosely covered, up to 1 day.
Run the tip of a paring knife around edge to loosen. Dip mold into a bowl of lukewarm water for several seconds. Pat mold dry, and invert onto a serving plate. Garnish with tomatoes and basil.