In a small bowl, whisk together ½ cup of the olive oil with the basil, mint, garlic, ½ teaspoon salt, black pepper, and pepper flakes. Add the butter beans, stir to coat, and set aside to marinate.
In a large skillet, heat the remaining ⅓ cup olive oil over medium-high heat. Pat the artichokes completely dry with paper towels and season with salt. When the oil shimmers, add half the artichokes in an even layer. Cook until charred on the bottom, about 6 minutes, then flip. Cook until the other side is charred and the artichokes are crispy, another 6 minutes or so. Transfer to paper towels to drain and repeat with the remaining artichokes, adding more olive oil to the skillet as needed.
On a serving platter, swoop and swirl the Greek yogurt across the surface. Scatter the artichokes on top, then spoon the butter beans and herb oil evenly over the yogurt. Serve with a sprinkle of mint leaves, a pinch of pepper flakes, and lemon wedges for squeezing.
