How to Make It
In a bowl, whisk the shallot and vinegar with a generous pinch each of salt and pepper; let stand for 5 minutes. Whisk in the mayonnaise, tarragon and 1 1/2 tablespoons of water. Season the béarnaise sauce with salt and pepper.
Light a grill and brush with oil. Brush the portobello caps with oil and season with salt and pepper. Grill over moderately high heat, turning once, until lightly charred, 6 minutes. Transfer to a plate. Brush the tomato with oil and season with salt and pepper. Grill, turning once, until lightly charred, 3 minutes total. Set the tomatoes on the portobellos.
Spoon the béarnaise on the tomato slices. Transfer the stacks to the grill and close the grill. Cook over moderate heat until the sauce is just hot, 3 minutes. Transfer to plates, garnish with scallions and serve.