Light a grill. In a small bowl, blend the butter with the tarragon and parsley and season with salt and pepper.
Brush the portobello caps with olive oil and season with salt and pepper. Set the mushrooms on the grill, gills down, and cook over moderate heat, turning once, until tender and nicely charred, about 8 minutes. Dollop the tarragon-parsley butter over the gills and cook for about 1 minute longer, until the butter is melted. Transfer the grilled mushrooms to plates and serve right away.