Combine 1 cup of the olive oil in a large bowl with 1 Tbsp. of the rosemary, the ginger, the balsamic vinegar, and the molasses. Whisk to incorporate, then season with salt and pepper and whisk again.
Add the green onions, tomato slices, and radicchio to the mixture, using your hands to gently coat. Let the vegetables marinate for at least an hour at room temperature.
In another bowl, combine the remaining ¼ cup olive oil with the remaining rosemary, the garlic, and generous amounts of salt and pepper.
Cut the venison roast into ¼-inch slices. Lay out a 24-inch sheet of plastic wrap on a counter and place two or three of the steaks on the plastic wrap, toward you, so that you can fold the wrap over the meat. Using the tenderizer side of a meat mallet, pound the meat into thin patties, then unfold the top layer of plastic, flip the meat, and do the same to the other side. Remove the pounded slices to the bowl containing the oil-garlic mixture and continue with the remaining slices. Let the venison marinate, at room temperature, for about half an hour.
Prepare a medium-high fire in a grill. Arrange the vegetables on the grill, cut sides down. Turn the radicchio and green onions occasionally, grilling until the edges are slightly charred, about 6 minutes for the onions and 8 for the radicchio. Grill the tomatoes for about 3 minutes per side, until blistered and a little charred. As they're done, transfer the vegetables to a platter and dash with salt and pepper.
Arrange the venison slices on the grill and cook quickly, for barely 2 minutes per side, until medium rare. Add to the platter with the vegetables and serve.