Salted Brown Butter Cookies

Cookies:

• 1 1/2 sticks (3/4 cup) unsalted butter, cut into pieces
• 2 cups all-purpose flour
• 1/4 cup cornstarch
• 3/4 cup packed light brown sugar
• 1 large egg
• 3/4 teaspoon fine sea salt
• 1 teaspoon vanilla

Icing:

• 1 (1-pound) box confectioners' sugar
• 4 teaspoons powdered egg whites (not reconstituted), such as Just Whites, or meringue powder (see Cooks' notes)
• 1/3 cup water
• 1 teaspoon fresh lemon juice
• 1 teaspoon vanilla

Garnish:

• Decorative sugars and or salts, if desired