Heat oven to 375°F.
In a large saucepan, cover the eggs with cold water and bring to a boil over high heat. Remove from the heat and let the eggs stand in the hot water for 10 minutes. Transfer the eggs to an ice water bath until chilled, about 5 minutes.
Meanwhile, line a rimmed baking sheet with parchment paper. Lay the ham flat, then bake until fat turns golden and meat is darker, about 15 minutes. Carefully transfer ham to paper towels to drain (it will crisp as it cools). When cool enough to handle, crumble into small bits.
In a blender, combine mayonnaise, goat cheese, mustard, and 1 teaspoon tarragon. Peel the eggs and halve them lengthwise. Add the yolks to the blender and puree smooth. Season to taste with salt and pepper.
Set the egg whites on a serving platter. Scrape the egg yolk mixture into a pastry bag fitted with a large round tip and pipe the filling into the whites. Top each egg with crispy ham and sprinkle with remaining 1 teaspoon of tarragon. Serve chilled.