Preheat oven to 450 degrees. Make a bed of the sliced onion in a large baking pan. Whisk balsamic and EVOO together, pour over onions and toss to coat.
Sprinkle the meaty side of the brisket generously with salt and coarse ground pepper. Turn brisket over and lay on top of onions, fat side up. Evenly season the top of the brisket with Seneca Seasoning and rub into the meat.
Bake uncovered for 15 minutes. Remove the baking pan and cover tightly with foil. Lower oven temperature to 325. Return covered pan to the oven and bake for 1 ½ hours.
Remove pan from oven and let rest (still covered) for 15 minutes. Uncover and let rest for an additional 15 minutes before slicing brisket across the grain. To plate, drizzle meat with pan juices and top with onions.