For the potatoes: Place the potatoes, 2 tablespoons of the butter, garlic and 1 tablespoon salt in a large saucepan. Add enough cold water to cover the potatoes by 1 inch. Bring to a boil over medium-high heat. Simmer until tender, 15 to 20 minutes. Remove the garlic cloves. Drain the potatoes in a colander. Place the potatoes back into the saucepan. Add the remaining 4 tablespoons butter and the half-and-half. Using a hand masher, mash the potatoes until smooth. Stir in the zest, chives, parsley, thyme, the remaining1 teaspoon salt and 1/2 teaspoon pepper. Keep warm over low heat.
For the shrimp: In a medium nonstick skillet, heat the butter over medium-high heat. Add the shrimp and sprinkle with the salt and pepper. Cook until the shrimp are cooked through, about 3 minutes. Using a slotted spoon, remove the shrimp and set aside. When cool enough to handle, chop the shrimp into 1/2-inch pieces. Stir the shrimp and any pan juices into the potatoes.
Transfer to a bowl and serve.