- Combine kosher salt and 4 cups water in pot and place over medium heat. Bring to simmer and stir until salt dissolves. Remove from heat and place lid on pot. Cool to room temperature.
- Combine remaining 4 cups water with lemon juice.
- Peel Jerusalem artichokes. Place in water once peeled to keep from turning brown. Cut into ½-inch cubes, return to water.
- Drain Jerusalem artichoke cubes and place in salt solution. Cover and let sit overnight in refrigerator.
- Combine rest of ingredients in medium pot and bring to simmer. Stir until sugar dissolves. Drain Jerusalem artichokes and add to pot. Continue to simmer for 3 minutes.
- Let cool completely then place in sealed container in refrigerator for 1 week before serving. Store in refrigerator for up to 1 month.