In the bowl of a standing electric mixer fitted with the paddle attachment, beat the butter and sugars together on medium speed until light and creamy.
Beat in the salt, tarragon, lime zest and juice on medium speed until combined, about 30-40 seconds.
Add the flour on low speed and beat until just combined, scrape down the bowl as needed.
Chill the dough for about 1 hour.
Preheat the oven to 350F (175C).
Line 2 baking sheets with parchment.
Using a small (2") scoop form dough balls and gently press flat as you place on baking sheets.
Place the dough balls about 1" apart-you should have 12 cookies on each sheet.
Bake for 13-15 minutes, until edges just start to turn light brown.
Remove to wire racks and cool cookies.
White Chocolate Frosting
Melt the chopped white chocolate, either using short bursts in a microwave or on top of the stove using double boiler method.
Using a small offset spatula frost the cookies and lightly sprinkle with lime zest.
Allow the frosting to firm up before serving.
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