Place a rack in the upper third of your oven and preheat the oven to 400 degrees F. Lightly coat an 8x8-inch baking dish or similar 2-quart casserole dish with nonstick spray and set aside.
Arrange the bread slices in a large rimmed baking sheet (you can leave it unlined or line it with parchment paper for easy cleanup). Brush 1/2 tablespoon of the oil over the first sides of the slices. Flip the slices over and brush the second sides with the remaining 1/2 teaspoon oil. Place in the oven and bake for 5 minutes. Remove the pan from the oven, flip the slices over, then return to the oven and continue baking until lightly toasted, 5 to 6 additional minutes. Set aside to cool. Reduce the oven temperature to 350 degrees F.
In the bowl of a standing mixer fitted with the paddle attachment or a medium mixing bowl, beat the cream cheese, Greek yogurt, garlic, Italian seasoning, red pepper flakes, and salt together on medium speed until smooth and combined, about 1 minute. With a rubber spatula, fold in the mozzarella, artichoke hearts, three-quarters of the cherry tomatoes, half of the bell peppers, and half of the olives, reserving the rest to sprinkle on top. Spread the mixture evenly in the prepared baking dish.
Scatter the salami and remaining tomatoes, bell peppers, and olives evenly over the top. Sprinkle with the Parmesan. Bake 25 to 30 minutes, until bubbling and hot throughout. Sprinkle with the basil. Serve hot with the toasted bread slices.