Preheat the oven to 425 degrees F.
Place the tomatillos, garlic and onion in a single layer on a baking sheet. Drizzle the vegetables with the 1 1/2 tablespoons of olive oil. Season with salt and pepper. Roast the vegetables in the oven until browned and softened, about 15 to 20 minutes.
Remove the vegetables from the oven and put the tomatillos and onion in a food processor. Squeeze the garlic cloves out of their peels into the food processor. Add the verjus, vinegar, and parsley leaves. Pulse until the mixture is pureed, drizzling in the 1/4 cup olive oil to thin dressing. Season the dressing with salt and pepper to taste, and set aside.
To complete salad: Arrange tomatoes, cheese and crabmeat, alternating to create a stack on serving plates. Drizzle the top with the dressing.