Vietnamese Fried Eggs

Name: Vietnamese Fried Eggs
Ingredients: Ice; 1/2 large fennel bulb, cored and very thinly sliced on a mandoline, plus fronds; 1/2 cup fresh lime juice; 1/4 cup Asian fish sauce; 1/4 cup sugar; 1/3 cup minced scallion; 1 tablespoon toasted and ground sesame seeds; 1 Thai red chile, minced; 1 large garlic clove, minced; 1 tablespoon peanut oil, plus more for frying; 4 large eggs; 2 cups lightly packed cilantro leaves; 2 cups lightly packed mint leaves; 1 small orange bell pepper, cut into julienne; 1/2 English cucumber—halved lengthwise, seeded and cut into julienne; 2 tablespoons unseasoned rice vinegar; Crispy Shallots, for serving (see Note)