Combine all the ingredients for the black pepper lemon syrup in a saucepan.
Bring it to a boil and simmer until it has a thin syrup consistency and a yield of about 1 cup.
Let it cool down to room temperature.
Strain the mix (to remove the black pepper), and set aside for the next step.
Making the Tequila Solution
Combine 1 cup of the spiced lemon syrup with the tequila.
Add the Xanthan gum and using an immersion blender (or a regular blender), blend the mix for a few minutes until it thickens and the Xanthan gum has dissolved and dispersed.
Add the Calcium lactate and blend further for a few minutes.
Cover and leave it to rest overnight in the fridge.
Sodium Alginate Bath
Combine the distilled water, sugar and Sodium Alginate and blend for a few minutes until the sodium alginate has completed dispersed in the solution and the solution has thickened.
Cover and let it rest overnight in the fridge.
To make the spheres
Set up your work space, with the tequila solution in one container, Sodium alginate solution in another, distilled water (to wash the spheres) in another container and the serving dishes.
Using your 1 tbsp measuring spoon, take about ½ tbsp of the tequila solution. Lower and drop it into the alginate solution in one smooth motion (See Notes). Swirl the bath gently if the sphere does not sink to the bottom of the bath. Leave it for 4- 5 minutes, and then take it out using the slotted spoon. (You can make more than 1 sphere at a time, just make sure they are not too close together, or they will stick to each other).
Transfer to the distilled water to rinse off the alginate, and then transfer it to your serving spoon/dish using the slotted spoon. Test the first sphere, to make sure the membrane is sturdy enough. If not, leave it in the sodium alginate bath a little longer.
Sprinkle some salt, pepper and raspberry powder (optional) on top and serve.
Serving Suggestion
For an even more exciting serving suggestion, pour chilled Vodka (even flavoured Vodka) into shot glasses and add one of these spheres into it. And serve with a slice of lime and salt on the rim.
Notes
Dropping the tequila solution into the alginate bath - You want to drop the tequila solution in one smooth motion. If you go too slow, a part of the tequila solution will drop to the bottom of the bath while you're still transferring, and this way you will not get nice oval or spherical shapes. If you go too fast however, the sphere might just float at the top. If that happens, gently swirl the bath so that it sinks to the bottom.