Earl Grey Tea Sugar Cookies

Ingredients

• 3 c (227 g) unsalted butter, softened
• 1¾ c (350 g) granulated sugar, divided
• 1 (50 g) large egg
• 2¼ cups (281 g) all-purpose flour
• 2 Tbsp (12 g) finely ground loose leaf Earl Grey tea, divided
• + ¾ tsp
• 1 tsp (2 g) grated lemon zest
• ½ tsp (2.5 g) baking powder
• ½ tsp (2.5 g) kosher salt
• 1 tsp (4 ml) vanilla extract
• ¼ c (60 ml) Earl Grey tea, strongly brewed
• 2¼ c (270 g) confectioners' sugar
• ½ tsp (2 ml) vanilla extract