Divide the cauliflower into florets, keeping the colours separated.
Take a large pot and pour in the vinegar, the water, salt and sugar. Stir to dissolve the salt and the sugar, then put it on the stove and bring it to a boil.
Blanch the florets for a few minutes, until they are al dente: this means they should be quite soft, but with a bite. Cook the white cauliflower first, then the green cauliflower and finally the purple one.
Remove the cauliflower florets from the pot with a slotted spoon and place them onto a clean cloth, leaving them to dry until the next day.
Arrange the colourful florets in layers in sterilized jars, adding a clove of garlic and a few grains of black pepper in each jar. Press well the florets as to fill up any empty space.
Pour in extra virgin olive oil to cover the florets completely. Check again after a few hours to see if you need to pour in more olive oil to completely cover the artichokes. Close the jars and store them for a few months in the pantry, or in a dry, cool and dark place. Be patient and keep them aside for at least 15 days before tasting them.