Make the black pepper syrup: Toast peppercorns; set aside to cool. Coarsely grind peppercorns, then combine in a large container with amaro and vodka. Let steep for at least 2 hours, then strain through a coffee filter. Store in a cool, dark place.
Make the sorghum coffee: Combine ingredients until sorghum is fully incorporated into coffee.
Assemble the drink: In a mixing glass filled with ice, combine all ingredients except soda and stir well. Strain into a highball glass filled with fresh ice, top with soda, and garnish with lemon peel.