Preheat grill to medium high or heat a grill pan over medium-high.
Remove portobello gills and trim stems. Brush mushrooms with 1 Tablespoon oil. Season with salt and pepper; set aside.
Cook shallots in 1 Tablespoon oil in a saute pan over medium-low heat until shallots begin to brown, 3-5 minutes. Add broth, port, Worcestershire, and Dijon. Bring to a boil over high heat; reduce sauce by half, about 15 minutes. Season sauce with salt and pepper.
Grill mushrooms uncovered, until grill marks appear and mushrooms are softened, 2 minutes per side. Slice mushrooms into 1/2-inch-thick strips and serve with sauce drizzled on top (if sauce thickens too much, thin out with additional 1-2 Tablespoons beef broth).
(optional) Garnish mushrooms with parsley and serve with a fresh salad on the side.