Using an electric mixer, cream 2 sticks butter with sugar until fluffy, about 2 minutes. Add ricotta, lemon zest and 4 teaspoons vanilla and beat well. Beat in the eggs one at a time. Scrape the sides of the bowl down with a rubber spatula, then beat in flour, baking soda and salt. Cover dough and chill for at least 2 hours and up to a week.
Heat oven to 350 degrees and line several cookie sheets with parchment paper or nonstick liners. Shape tablespoons of dough into balls. Place 2 inches apart on baking sheets and bake until pale golden on the bottom, about 12 to 14 minutes. Let cool on wire racks.
Melt remaining 2 tablespoon butters. Whisk confectioners’ sugar to break up any large lumps, then whisk in melted butter, lemon juice, remaining 1½ teaspoons vanilla and enough milk to make a spreadable icing. Spread icing on cooled cookies, then let set for at least 20 minutes before serving.
Recipe by Allons-Eat! at https://www.allonseat.com/gluten-free-lemon-ricotta-cookies/