Toast the walnuts in a dry skillet over medium heat for 3-4 minutes, stirring occasionally, until fragrant and lightly golden. This brings out their natural oils and deepens their flavor, which is crucial since they're a textural and flavor component in this dip. Transfer to a cutting board, let cool slightly, then finely chop and set aside.
Coarsely grate the radishes using a box grater or food processor, then place them in a clean kitchen towel and squeeze firmly to remove excess moisture—this prevents the tzatziki from becoming watery. While the radishes drain, finely mince the garlic and finely chop the fresh dill. This prep work ensures all ingredients are ready to combine without delay.
In a bowl, combine the yogurt with the lemon juice, lemon zest, garlic, salt, and black pepper. Whisk gently to blend the aromatics and acid throughout—I like to let these flavors marry for a minute before adding the vegetables, as it helps distribute the seasoning more evenly. Add the squeezed radishes and toasted walnuts from Steps 1 and 2, then fold gently until just combined, being careful not to overmix.
Drizzle the extra virgin olive oil over the top of the tzatziki and fold in the chopped dill from Step 2, reserving a small pinch for garnish if desired. Taste and adjust seasoning with additional salt, pepper, or lemon juice as needed. I find the tzatziki benefits from resting in the refrigerator for at least 15-30 minutes before serving, which allows the flavors to meld beautifully.