Preparation

• Cook the bacon in a 12-inch nonstick skillet over medium heat, stirring occasionally, until crisp, 4 to 5 minutes. Use a slotted spoon to transfer the bacon to a paper-towel-lined plate, leaving any fat behind in the skillet.
• Meanwhile, combine the grated Parmigiano, vinegar, and 1/4 tsp. each salt and pepper in a medium bowl. Gradually whisk in the olive oil.
• Put the skillet over medium-low heat and add the vegetable oil. When the oil is hot, crack the eggs into the skillet and cook, basting the whites occasionally with the fat, until the whites are set but the yolks are still runny, 2 to 3 minutes.
• Meanwhile, in a large bowl, toss the greens, tarragon leaves, peas, and radishes. Lightly dress the salad with some of the vinaigrette, season with a generous pinch each salt and pepper, and toss. Divide the salad among four serving plates.
• Top each salad with an egg. Drizzle 1/2 Tbs. vinaigrette over each egg, and season with salt and pepper. Top with the bacon, shaved Parmigiano, chives, and chopped tarragon. Serve the remaining vinaigrette on the side.