In a large bowl, with an electric mixer on medium, beat butter and granulated sugar until pale and fluffy, about 2 minuted. Beat in both extracts, and salt. Gradually add flour and mix on low until just combined. divide the dough in half. Knead food coloring into one half until desired color is reached ( you might want to use gloves for this part). Form dough into disks, wrap each disk in plastic, and refrigerate 20 minuted up to overnight. (Dough can be frozen up to 1 month; thaw in the refrigerator before using.)
Divide untinted dough into 12 pieces. On a lightly floured surface, shape each into a 12-inch long log. Refrigerate until firm but pliable, about 10 minutes. Repeat with tinted dough. Twist a tinted and untinted piece together; roll gently to form a log. Cut crosswise into 2 equal pieces and bend one end to form a cane.Repeat. Arrange on parchment-lined sheets, about 2 inches apart. Cover with plastic wrap and chill 1 hour and up to overnight.
Preheat oven to 325 degrees. Bake, rotating sheets halfway through, until cookies are firm but not taking on any color, 20 to 24 minutes. Transfer sheets to wire racks and let cool completely.
Brush each candy cane with egg white and sprinkle with sanding sugar; tap off excess. (Cookies can be stored in an airtight container at room temperature up to 1 week).