How to Make It
For the turmeric-chile mixer: Puree turmeric root and 1/4 cup water in a blender until smooth. In a small saucepan, combine the turmeric puree, granulated sugar, and 3/4 cup water; bring to a boil, stirring to dissolve sugar. Turn off heat, and let steep 2 hours. Pour mixture through a fine wire mesh strainer; discard solids. Soften dried chiles de arbol in a small amount of warm water. Puree chiles with 1/4 cup fresh lime juice. Stir together turmeric mixture, chile puree, and 3/4 cup fresh lime juice; chill 1 hour.
For the cocktail: Pour mescal and tequila into an ice-filled cocktail shaker. Add 2 Tbsp. turmeric-chile mixer; shake vigorously until well chilled, about 30 seconds. Strain into a glass rimmed with lime juice and a mixture of equal parts salt and Indian red chili powder. Garnish with a lemon slice.