Cover potatoes with water in a pan. Add 1 tablespoon salt, and bring to a boil. Reduce heat, and simmer until tender, about 10 minutes. Drain potatoes and halve lengthwise.
Heat oil in a large skillet over medium heat. Add shallot and garlic, and cook until soft, about 2 minutes. Add potatoes, cut sides down, and cook until golden brown, about 10 minutes.
Stir in stock, wine, and 1/2 teaspoon salt. Cook until liquid is reduced by a third, about 2 minutes.
Remove from heat. Add thyme and butter, and stir until butter has melted. Stir in lemon juice, salt, and pepper.