Toast walnuts in a dry skillet over medium heat, stirring occasionally, until fragrant and lightly golden at the edges, about 5 minutes. Spread on a plate to cool completely.
In a food processor or blender, combine cooled walnuts, garlic cloves, lemon juice, Dijon mustard, salt, and pepper. Pulse a few times to break up the walnuts into small pieces.
With the motor running, slowly drizzle in olive oil through the feed tube (or just off-center of the bowl) until the mixture is smooth and emulsified, about 1–2 minutes. Scrape down sides as needed.
Add water one tablespoon at a time until desired consistency is reached—the mixture should spread easily but not run like dressing. Taste and adjust salt or lemon juice if needed.
Transfer to an airtight container and refrigerate for at least 1 hour before using so flavors meld together.
