For the byaldi: Preheat the oven to 400 degrees F. Place the vegetable oil, butter and onions in a large pot set over medium-high heat. Sprinkle with 1 teaspoon salt and cook until the onions start to brown and caramelize. Spread the onions in an even layer on the bottom of an 8- by 8-inch or similar sized dish. Fan out each vegetable in rows, alternating zucchini, eggplant, squash and tomatoes all the way down the dish until the onions are covered with the vegetables. Sprinkle with salt, pepper and the thyme leaves and then drizzle a bit of olive oil over the top. Bake in the oven until the vegetables are tender, 20 to 30 minutes. Remove from the oven and keep in a warm place.
For the chimichurri sauce: Make the chimichurri sauce by combining the olive oil, mint, oregano, parsley, sherry vinegar, lime juice, shallot and garlic in a bowl. Mix all the ingredients together and season with salt and pepper. Set aside.
For the steak: Heat 2 tablespoons vegetable oil in 2 large pans over high heat. Mix the coriander, cumin and peppercorns together into a spice blend. Season the flank steak on all sides with some salt and spice blend. Once the oil is almost smoking, add 2 pieces of flank steak to each pan. Reduce the heat to medium and saute until a nice crust is formed. Flip the meat and saute on the other side. If you have thick pieces of flank steak or prefer it cooked more than medium rare, you may put the steak in the oven with the byaldi to finish cooking. Once the steak has a nice sear and is cooked to the desired temperature, transfer to a cutting board to rest for 3 to 4 minutes.
Slice the meat against the grain in slices about 1/4-inch thick. Place each sliced portion on a plate, season with a little salt and pepper and drizzle the chimichurri sauce over the steak. Serve the byaldi family style in the middle of the table.