Cut the tomatoes in half and place in a sieve with a bowl beneath. Squeeze each tomato half with your hands to express as much juice and pulp as possible. There should be about 1/2 cup.
Put the tomato juice and pulp into a food processor or blender, and add the salt, garlic clove, mustard, and Chile Lime shrub. Pulse several times to make sure the garlic is well chopped.
With the machine running, slowly drizzle in the olive oil. Pour the dressing into a jar or other container with a lid. Let the dressing sit, unrefrigerated, for about 30 minutes prior to serving to ensure the flavors are well developed.