For the Herb Syrup:
Combine 1 quart of water and 1 quart of sugar in a pot over medium to high heat and stir to dissolve. Bring to just before a boil, then take off the heat and add the rosemary, sage, and thyme. Cover and let steep for 20 minutes. Strain and add salt to taste. Let cool, bottle, and refrigerate between uses.
To Assemble and Serve:
Muddle the cucumber, herb syrup, salt, and 1 twist of freshly ground black pepper in a mixing glass. Add the gin, lemon juice, and ice, and lightly shake. Strain into a flute glass and top with Cava. Twist a lemon peel over the glass and discard.