Gammy Brown's Deviled Ham from 'The Great Meat Cookbook'

Ingredients (10)

• 1 tablespoon olive oil
• 1/4 cup chopped shallots
• 2 1/2 cups 1/2-inch-diced leftover ham
• 1/2 cup finely chopped celery, including leafy tops
• 1/4 cup chopped fresh flat-leaf parsley
• 1 tablespoon prepared horseradish, or more to taste
• 2 tablespoons Dijon mustard, or more to taste
• 1/3 cup mayonnaise, or more if needed
• 1/4 cup finely chopped dill pickles, sweet pickles, or cornichons (optional)
• Freshly ground black pepper