Pesto Egg Salad Toasts

Name: Pesto Egg Salad Toasts
Ingredients: 6 large eggs; ¼ cup chopped walnuts; 1 clove garlic, grated (1/4 tsp.); 3 tablespoons olive oil, divided; 2 tablespoons finely grated Parmesan cheese, plus more for serving; ½ teaspoon kosher salt, divided; ¼ cup finely chopped basil, plus more for serving; 1 ½ teaspoons fresh lemon juice (from 1 lemon), divided; ⅓ cup plain whole-milk strained yogurt, such as Greek; 3 cups packed baby arugula; 4 1/2-in.-thick slices sourdough bread, toasted; Freshly ground black pepper, for serving