Combine the yogurt, olive oil, lemon juice, and garlic in a medium bowl.
Roll the grated cucumber up into a paper towel and squeeze it firmly over your sink to remove the excess moisture.
Add the cucumber to the bowl with the other ingredients and stir to combine. Divide this base mixture into two smaller bowls.
To one bowl add the chopped dill, parsley, cilantro, and mint. Stir to combine.
To the second bowl, add the honey, ginger, and turmeric. Stir to combine.
Cover both yogurt dips and refrigerate them until you're ready to use them.