Bring a small sauce pot of water to a boil and fill a small bowl with ice water. Carefully lower the eggs into the boiling water and cook for exactly 5 minutes for runny yolks (for firmer yolks, cook 1 to 4 minutes longer). Transfer the eggs to the ice water to cool. Carefully peel the eggs. While the eggs cook, prepare the chicken.

• Pat the chicken dry with a paper towel; season generously with salt and pepper.
• Strip enough thyme leaves from the stems to measure ½ teaspoon [1 tsp]. Save any remaining thyme for another use.

In a small bowl, stir together the thyme and 1 tablespoon [2 TBL] oil. Rub the chicken all over with the thyme oil.

In a large frying pan over medium-high heat, warm 1 to 2 teaspoons oil until hot but not smoking. Add the chicken and cook, turning once, until lightly browned, 1 to 2 minutes per side. Reduce the heat to medium-low and continue cooking, turning occasionally, until firm and cooked through, 5 to 8 minutes. Transfer to a plate. Wipe out the pan.

• Trim the root ends from the scallions; thinly slice the scallions.
• Snap off the woody ends from the asparagus.

In the same pan used for the chicken, warm 1 to 2 tablespoons oil over medium-high heat until hot but not smoking. Add the scallions and asparagus in a single layer, season with salt and pepper, and cook, turning the asparagus occasionally and stirring together with the scallions, until the asparagus is crisp-tender and the scallions have softened, 3 to 5 minutes.

While the vegetables cook, prepare the mustard vinaigrette.

• Juice half the lemon; cut half into wedges for garnish. [Juice 1 lemon; cut 1 lemon into wedges.]

In a small bowl, stir together the mustard, 2 teaspoons [4 tsp] lemon juice, and 1 tablespoon [2 TBL] oil. Season to taste with salt and pepper.

Transfer the chicken and asparagus to individual plates. Carefully cut the eggs in half over the asparagus. Drizzle with the mustard vinaigrette and serve with the lemon wedges.