Combine the rhubarb, sugar, and water into a large pot. Give a stir and bring to a boil over medium heat. Let simmer for 15 minutes. Add the thyme and simmer for an additional 5 minutes.
Remove from the heat and strain with a fine mesh strainer into a mason jar. Put the reserved rhubarb solids aside and keep for several days in the fridge if desired. Cool the simple syrup and keep for up to a week in the fridge.
Combine all ingredients except the thyme and ice in a cocktail shaker and shake vigorously for 30 seconds. Add ice, and shake for an additional 10 seconds. Strain into a coupe or your favourite glass, garnish with a sprig of thyme and enjoy!