Lavender-Lemon Sandwich Cookies

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For the cookies:

1 1/2 sticks (12 tablespoons) unsalted butter, at room temperature

1 cup granulated sugar

1/4 cup honey

1 large egg

1 teaspoon pure vanilla extract

Grated zest of 1 lemon

2 cups all-purpose flour

1 teaspoon baking soda

1/2 teaspoon salt

2 tablespoons dried lavender

1/2 cup coarse sugar

For the filling:

1 1/2 sticks (12 tablespoons) unsalted butter, at room temperature

Finely grated zest of 1 lemon, plus 2 tablespoons lemon juice

1/2 teaspoon pure vanilla extract

2 1/2 cups confectioners' sugar