Sweet Potato Gnocchi with Sage Butter

Name: Sweet Potato Gnocchi with Sage Butter
Ingredients: 3 pounds (1.4 kg) sweet potatoes (about 6 medium potatoes); 1 tablespoon (9 g) Diamond Crystal kosher salt; for table salt, use half as much by volume or same weight; 3 ounces (85 g) Parmigiano-Reggiano, finely grated, plus more for serving; 3 large egg yolks, lightly beaten; 1 1/2 cups all-purpose flour (6 3/4 ounces; 191 g), plus more for dusting and shaping; 8 tablespoons unsalted butter (4 ounces; 113 g), plus 1 tablespoon (1/2 ounce; 14 g) chilled unsalted butter for finishing; Leaves from 1 large sprig fresh sage (about 15 large and small leaves); 1 tablespoon (15 ml) fresh lemon juice, optional (see notes); Lemon zest, for serving; Aleppo pepper, for serving