How to Make It
Slice the shallot in half. Finely chop one half; thinly slice the other. Set aside.
Combine the ground sirloin, ¼ teaspoon each salt and pepper, the chopped shallots, and 1 tablespoon of the mustard in a bowl. Form into 4 patties and set aside.
Heat 2 tablespoons of the oil in a large nonstick skillet over medium-high. Add the potatoes in a single layer and cook undisturbed, 4 to 5 minutes. Add the green beans and the remaining salt and pepper. Cook for another 10 minutes, stirring occasionally, until the potatoes are soft and the green beans are crisp-tender.
Meanwhile, heat another skillet over medium-high. Add the burgers and cook for 4 to 5 minutes per side for medium-rare. Divide the remaining mustard evenly among the rolls. Toss the herbs and sliced shallots with the remaining oil and the lemon juice. Serve on top of the burgers with the vegetables on the side.