Spring Vegetable Panzanella with Poached Eggs

Name: Spring Vegetable Panzanella with Poached Eggs
Ingredients: For the panzanella:; 4 tablespoons extra-virgin olive oil, divided; 1 baguette or 1 small loaf of ciabatta (225 grams), cut into 1-inch cubes (between 3 and 4 cups); 1 teaspoon salt, plus more to taste; 1 leek, white and light green parts only, cut crosswise into very thin circles or half-moons, cleaned, and dried; 1 bunch asparagus (340 grams), woody ends snapped off and cut into 1 1/2- to 2-inch pieces; 2 1/2 cups (380 grams) English peas, fresh or frozen and thawed; 2 large handfuls (220 grams) snow peas, ends trimmed; 1 splash (1 to 2 teaspoons) balsamic vinegar; Juice of half a lemon; Pepper, to taste; 1 cup small, uneven cubes Parmesan; Eggs, 1 or 2 per person, for poaching (optional); For the pesto:; 1 1/2 cups loosely packed fresh basil leaves; 1/2 cup loosely packed fresh mint leaves; 3 to 4 sprigs fresh thyme, stripped; 2 tablespoons walnuts; 1 or 2 cloves garlic, peeled and smashed; 1/4 cup extra-virgin olive oil; 1/4 cup finely grated Parmesan; Salt, to taste