Preheat the oven to 425°F. On a large, rimmed sheet pan, toss the potatoes with the garlic and the 2 tablespoons olive oil. Season with 1 teaspoon salt and 1/2 teaspoon pepper. Roast until golden and crisp on the outside and soft in the center, 20 to 30 minutes depending on size, shaking the pan to toss the potatoes halfway through cooking. Let cool, then transfer to a serving bowl.
Meanwhile, in a skillet over medium heat, warm the remaining 1/4 cup olive oil. Add the whites of the green onions and cook for 4 minutes. Reduce the heat to low, stir in the parsley, mustard, and lemon juice, and warm through, 2 to 3 minutes. Remove the dressing from the heat, stir in the peppers and the greens of the green onions, then pour over the potatoes. Stir to combine, season to taste with salt and pepper, and serve warm or at room temperature.