This is essentially a fancier, subtler gimlet. The key thing here is chamomile syrup, which shouldn’t intimidate you, because it’s just simple syrup with a chamomile tea bag.
More explicit directions: boil one cup of water. Toss in two bags of chamomile tea; the folks at Grey Goose probably wouldn’t mind you using the most expensive chamomile you can get your mitts on. Steep for a long time and make that tea strong. Then, bring it to a boil again (if it’s no longer a cup, top it up with hot water) and stir in one cup of sugar.
2 oz. Grey Goose Original
3/4 oz. fresh lime juice
1/2 oz. homemade chamomile syrup
Lime zest spiral to garnish
Add ingredients to shaker with ice. Shake and double strain into a coupe and garnish with lime spiral.