In a medium bowl, combine sugar and lime zest. Mix and set aside.
In a large mixing bowl with an electric mixer fitted with a paddle attachment, beat on medium speed until butter is smooth, about 3 minutes. Add sugar with lime zest. Beat for another 2 minutes. Add vanilla bean paste, lime juice and salt. Beat until the mixture is creamy and fluffy. Scrape down the sides of the bowl. Turn the mixer to low speed, add the flour in 3 additions. Mix until just incorporated and dough starts to come together, scraping bowl if necessary. Cover the mixing bowl with plastic wrap and chill in the fridge for 1 hour.
Preheat oven to 350˚F (177˚C). Arrange racks in lower and upper thirds of the oven. Line 2 baking sheets with parchment papers.
Shape the dough into 1-inch balls, about 15 grams each. Place them on a quarter baking sheet or large plate. Make an indentation into the center of each ball with a small finger, about halfway deep. Smooth out the dough if there are cracks. Cover with plastic wrap and chill in the fridge for 15 minutes.
Place the dough balls 2-inch apart on the prepared baking sheets. Fill each indentation with about ¼ teaspoon jam. Dough balls that do not fit can be baked for second round. Keep in the fridge with plastic wrap.
Bake in the oven for 15 – 17 minutes, rotating the baking sheets top to bottom and front to back after 8 minutes. Bake until the edges of the cookies are lightly golden brown. Transfer the baking sheets to counter and let the cookies rest on the sheets for at least 2 minutes. Transfer the cookies to racks and cool completely. Repeat with the rest of the dough.
If using glaze, in a medium bowl, add powdered sugar. Add 1½ tablespoons lime juice. Whisk until smooth. Add more juice if the frosting is too thick. Drizzle the glaze over the cooled cookies with a fork. Let them set at room temperature, about 30 minutes. Serve.