In a large pot, steam the potatoes in a steamer basket over boiling water until fork-tender, about 20 minutes. Set the potatoes aside; reserve 1/4 cup of the cooking water.
Meanwhile, using a food processor, pulse the garlic, walnuts and 1/2 teaspoon salt until coarsely chopped. With the machine on, pour in 2 tablespoons lemon juice, then pour in the olive oil in a slow, steady stream to form a paste.
Transfer the potatoes to a standing mixer and add the reserved cooking water. Mash the potatoes on medium speed until smooth. Add the garlic-walnut paste and mix until combined. Mix in the remaining 1 tablespoon lemon juice and season to taste with salt. Serve with the lemon wedges.