Cream the butter and sugar in an electric mixer until light and fluffy.
Add the salt and vanilla and beat until just blended.
With the mixer on low, beat in the flour until the dough is smooth and comes together.
Chill the dough in the fridge for at least 3 hours, or up to 24 hours.
Preheat the oven to 325°F. Line a baking sheet with parchment paper.
Roll the dough out on a floured surface to 1/8”-inches thick. Use a heart cookie cutter to cut out heart shapes and place them on the lined cookie sheet.
Bake the hearts for 18 to 20 minutes, or until the hearts are lightly golden around the edges. Allow to cool completely before glazing.
Whip the glaze ingredients together in a bowl. Add up to 1 tablespoon more water as needed to make the glaze thin enough to spread.
Spread the glaze on the cooled cookies and cover with sugar.