Make the botanical-infused vodka: In a sous-vide cooking bag, combine the vodka with the juniper, lemon peels, lime peels, grapefruit peels, cardamom, rose petals, lavender, cucumber peels, tarragon, dill, cinnamon and pink peppercorns.
Place in 150° water and cook for 40 minutes. Remove the bag from the water and cool to room temperature, then open and filter the liquid several times through a coffee filter until the liquid is clear.
Make the tonic water: In a rechargeable soda siphon, add the baking soda, quinine powder and the simple syrup. Fill with ice-cold water, seal and carbonate. Stored in the refrigerator, the tonic water will keep for 2 to 3 days.
Make the cocktail: In a Collins glass, add the large ice cubes. Add the botanical-infused vodka and the lime juice. Fill the glass with the homemade tonic water. Stir once with a barspoon. Garnish with the lime wedge and serve.