Add oil to a large saucepan and heat over medium. Add the water, tomatoes, onion, garlic, beetroot, carrot, Worcestershire sauce, salt, and pepper. Cook on medium heat for about 35 to 45 minutes, or until vegetables are soft (stirring now and again). Remove vegetables from heat and set aside to cool.
Once cooled to room temperature, work in small batches (about 2 cups at a time) to puree the vegetables with their liquid in a high-speed blender. To the final batch, add the dates, horseradish (if using), cucumbers, basil and lime juice. Process on high speed until mixture is smooth.
Transfer all of the pureed vegetable juice to a large pitcher and stir with a wooden spoon several times. Chill the pureed vegetable juice in the refrigerator for at least 4 hours before serving.
To serve, pour 1 cup of the vegetable juice mixture into a tall glass. Add ice and 1-ounce vodka, if desired. See ideas for building your own Blood Mary Bar below.
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Bloody Mary vegetable juice base can be made up to two weeks in advance and frozen.