Bring a small pot of water to a boil.
Place the shallots, sugar, vinegar, salt, beets, and bay leaf in a metal or glass bowl. Place bowl on top of the open pot (this is called a bain-marie or double boiler). Reduce heat to medium.Cover and cook for 30-35 minutes, stirring regularly.
Using a 250 micron superbag, strain the juice. Save the leftover steamed shallots for future uses, such as sauces or stocks.
Mix together 200g of the shallot liquid and sodium citrate in a blender on low speed.
With blender still on, sprinkle in the sodium alginate. Continue blending for two to three minutes.
Pour the mixture into a covered container and let it sit while the sodium alginate hydrates. Allow the mixture to settle until all the air bubbles have been released. The hydrating and air bubble release process could take up to 24 hours, so be sure to not rush this process.
Pro tip: you can replace the sodium alginate with double the amount of Sphere Magic and the solution will be ready within an hour. Also, you can skip the blender and use a whisk to avoid unwanted air bubbles
Mix distilled water with the calcium chloride until it dissolves completely.
Fill a spherificator with the shallot liquid, let the spherificator dispense the spheres into the setting bath.
Using a spherification spoon, stir gently for 30-45 seconds. Stir the bath without touching the spheres.
Transfer spheres to the rinsing bath and stir gently.
Remove spheres from the rinsing bath with a spherification spoon and blot dry on paper towels before serving.
These spheres are best served immediately. You may store them for a brief time in the remaining shallot spherification liquid. However, the skin on the spheres will continue to harden until the spheres are solid.