Cut each goat cheese log into 4 rounds. Gently press each round to 1/2-inch thickness on a baking sheet, and freeze 20 minutes.
Place the flour in a small bowl. Whisk together the egg and milk in a second small bowl. Combine the panko, salt, and pepper in a third small bowl. Dredge goat cheese rounds in flour, dip in egg mixture, and dredge in panko mixture until coated. Place on a plate, and chill until all goat cheese rounds are breaded.
Heat the vegetable oil in a large skillet over medium until hot. Add goat cheese rounds to skillet, and cook until golden brown on each side, 3 to 4 minutes total. Remove to a paper towel-lined plate.
To serve, arrange salad greens on a serving platter; top with strawberries, cucumber, onion, and goat cheese croutons. Drizzle with vinaigrette, and garnish with dill sprigs.