For the Lemon Thyme Syrup, mix sugar and water in small saucepan. Bring to boil. Add lemon thyme; simmer 5 minutes. Remove from heat. Let stand 10 minutes, stirring occasionally to dissolve sugar. Strain. Cover and refrigerate until well chilled. (This makes enough syrup for 8 cocktails.)
For each cocktail shaker of Lemon Blanc Cocktail, fill shaker half full with cracked ice. Add 2 tablespoons each gin and Limoncello liqueur, 1/4 cup each Meyer lemon juice and Lemon Thyme Syrup, 1/2 teaspoon vanilla and 1/4 cup half-and-half. (Be sure to add ingredients in order listed to avoid curdling of the half-and-half). Shake until well mixed and chilled. Strain into 2 cocktail glasses. Serve with or without ice. Garnish with lemon twists. Repeat with remaining ingredients to make 8 cocktails.