Preheat the oven to 400 degrees F. Line 2 baking sheets with parchment paper and coat with nonstick cooking spray.
Combine the oil, garlic, oregano and pepper flakes in a small bowl. Arrange the polenta, tomato and onion slices on the prepared baking sheets. Brush the tops of the polenta and vegetables with the herbed oil. Sprinkle the vegetables with 1/4 teaspoon salt and a few grinds of pepper. Roast until the vegetables are soft and beginning to caramelize, about 25 minutes.
Gently combine the ground beef with 1/2 teaspoon salt and a few grinds of pepper in a medium bowl. Shape into 8 patties about 2 1/2 inches across and 1/2 inch thick. Spray both sides with nonstick cooking spray. Heat a large nonstick skillet on high for two minutes and arrange the patties in the skillet spaced evenly apart. Reduce to medium high and cook for about 1 1/2 minutes per side for medium-rare. Allow patties to rest for 5 minutes before assembling sliders.
Assemble the sliders: On a work surface, place 8 polenta rounds herb-side down and top with 3 basil leaves, slightly overlapped on each. Top basil with a patty, tomato and onion slices. Sandwich with the remaining polenta rounds, herb-side up, and serve 2 sliders per person.
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