Grill one of the lemon halves cut-side down until charred, about 5 minutes. Let cool slightly, then squeeze the juice from it into a small bowl--you should have about 1 ounce. Cut a thick wheel of lemon from the other half and grill on both sides until charred, 3 to 5 minutes; set aside.
Add the lemon juice, Simple Syrup, gin and Scotch to a cocktail shaker, add large ice and shake vigorously. Add a fresh large ice cube to a highball glass with tongs and double-strain the cocktail into the glass over the cube. Top with the prosecco and garnish with the charred lemon wheel.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month.