Preheat the oven to 350 degrees F. Roast the peppers cut-side down on a baking sheet until wrinkled, about 30 minutes. Transfer to a bowl, cover and let stand 10 minutes. Peel off the skin with your fingers under running water. Cut each piece in half to make 8 pieces.
Spread the almonds on a baking sheet and bake until golden, about 10 minutes. Let cool, then roughly chop. Combine all but 1 tablespoon of the almonds in a small bowl with the chopped mint and parsley.
Make the vinaigrette: Whisk the vinegar, garlic, sugar, 1/2 teaspoon salt and a few grinds of pepper in another small bowl. Slowly whisk in the olive oil until emulsified.
Line four 4-ounce ramekins with plastic wrap, leaving an overhang. Place 1 tomato slice in each ramekin; sprinkle with salt and some of the vinaigrette and herb-almond mixture. Top with a layer of cucumber slices; sprinkle with more salt, vinaigrette and herb-almond mixture. Add 1 piece of roasted bell pepper to each ramekin; sprinkle with more salt, vinaigrette and herb-almond mixture. Repeat the layers, reserving 1 to 2 tablespoons of the vinaigrette.
Pull the plastic wrap taut around the vegetable stacks and cover with the overhanging plastic; transfer the ramekins to a baking dish. Weigh down each stack with a heavy can. Refrigerate until chilled, about 2 hours.
Open the plastic wrap; drain the excess liquid and invert the stacks onto plates. Toss the mint and parsley leaves with a drizzle of the reserved vinaigrette. Pile on top of the vegetable stacks. Sprinkle with the reserved chopped almonds and drizzle with more vinaigrette.