Using an electric mixer, cream butter with sugar until fluffy, about 2 minutes. Add ricotta, lemon zest and 1 1/4 teaspoons vanilla and beat well. Beat in the egg.

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 15 minutes. Let cool on wire racks.

Melt remaining 1/2 tablespoon butter. Combine with the lemon juice and the remaining 3/4 teaspoon vanilla. Sift confectioners’ sugar to break up any large lumps, and add to melted butter, in addition to enough milk to make a spreadable icing.

Spread icing on cooled cookies, then let set for at least 20 minutes before serving.