Combine the flour, salt, and tea. Depending on which brand of tea you use, you may want to grind the tea leaves further before adding.
Using a stand or hand mixer, cream the butter and sugars together until light and fluffy. Then, add the lavender syrup and mix until well combined.
Slowly add the dry ingredients, mixing continuously until a dough forms. If dough is too crumbly, you can add water a teaspoon at a time until dough can be loosely formed into a ball (slight crumble is expected).
Roll the dough into a log shape, approximately 1½-2 inches in diameter (4-5cm). Wrap in plastic wrap and refrigerate for 30 minutes.
Preheat oven to 350℉ (180°C / 160°C fan). Slice cookie dough into ¼ in (just over ½ cm) slices. Line a baking sheet with parchment paper, and place cookies on sheet with at least 1 inch of space in between (~2.5 cm).
Bake for 10-12 minutes. Cool on a wire rack.