Preheat the oven to 450˚. Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the artichoke hearts in a single layer and cook, turning, until browned, 2 to 3 minutes. Scatter the leek, ham and broccoli on top and cook, stirring, until the vegetables soften, 2 to 3 minutes; season with salt and pepper.
Line a rimmed baking sheet with foil. Unroll the pie dough on the prepared pan and gently flatten any curled edges. Spread the mustard on the dough, leaving a 1-inch border. Top with half the gruyere, then the vegetable mixture, then the remaining gruyere. Fold in the edges of the dough, pleating as needed. Lightly brush the crust with olive oil and sprinkle with pepper. Bake until the pastry is golden brown and the cheese melts, 20 to 25 minutes.
Meanwhile, thinly slice the radishes and combine in a large bowl with the mixed greens, vinegar and remaining 1 tablespoon olive oil. Season with salt and pepper and toss. Serve the galette with the salad.