Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with aluminum foil.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned and crispy, about 10 minutes. Drain bacon slices on paper towels and crumble when cool enough to handle.
Sprinkle naan flatbreads with 1/2 of the Gruyere cheese, leaving 1/2 inch border at the edges. Sprinkle with blue cheese and red onion and place on the prepared baking sheet.
Bake until flatbreads begin to brown, 7 to 9 minutes. Remove from the oven and sprinkle with blueberries, bacon, and the remaining Gruyere. Bake until the cheese has melted and the flatbreads are golden brown, about 2 minutes. Top with sliced basil and black pepper. Serve immediately.