Summer Bean Gribiche

Name: Summer Bean Gribiche
Ingredients: 1 lb. mixed snap beans (such as green, wax, and/or Romano), trimmed; ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, plus more; 5 large eggs; ⅓ cup extra-virgin olive oil; 3 Tbsp. white wine vinegar; 2 Tbsp. Dijon mustard; ½ tsp. freshly ground pepper, plus more; 1 large shallot, thinly sliced into rings; ¼ cup finely chopped cornichons; 2 Tbsp. coarsely chopped drained capers; ¼ cup coarsely chopped tender herbs (such as parsley and/or dill), plus more for serving