1. In a pot, bring 1 cup (250 ml) of water to a boil. Mix blueberries and sugar in and continue boiling for 2 minutes while stirring constantly.
2. In a rectangular, flat-bottomed bowl and using a hand blender, dissolve 1 sachet of sodium alginate in blueberry puree. Let sit for 10 minutes.
3. Remove from heat and blend. if you have an immersion blender, you can do this directly in the pot; if not, either let the mixture cool down a bit before you transfer it to your blender, or be extra careful not to let steam build up too much in the blender as you blend.
4. Dissolve 1 sachet of calcium lactate in 2 cups (500 ml) of water using a spoon. then, using a pipette held at a 90° angle, slowly drip droplets of the alginate solution into the calcium lactate bath. Let sit for 3 minutes, then empty the calcium lactate bath into the sink and onto a sieve so you’re left with just the blueberry caviar. rinse in lukewarm water.
5. Bring water to a boil and remove from heat. place tea bags in hot water and let sit for 5 minutes.
6. In a rectangular, flat-bottomed bowl, pour tea, and sprinkle in soy lecithin. Using a hand blender, blend for 3 to 4 minutes, then let sit for 5 minutes.
7. To serve, collect foam using a spoon. If needed and to obtain more foam, repeat step 5.
8. In a cocktail shaker, shake together rum, club soda, and lime juice. pour into a glass and add in a few blueberry pearls. Top first with a few mint leaves, then with the lavender foam, and serve.