Add the water, sugar, and lavender buds to a medium saucepan over medium heat. Bring to a simmer for 10 minutes.
Remove from heat and strain the syrup to remove the lavender particles.
Add the hot espresso to a 12 oz mug or 16-20 oz cold beverage glass.
Add 1-2 tablespoons lavender syrup to the espresso. (Allow remaining lavender syrup to cool before storing it)
If serving hot, steam the oat-milk via steamer, frother, or heat with the microwave and a handheld frother. Pour the hot frothed oat-milk over the espresso including the milk foam.
If serving cold, fill the gas with ice and add the cold oat-milk over the espresso.
Garnish with lavender buds if desired and enjoy