To make the vinaigrette:
- In a blender, combine the lemon juice, garlic,anchovies, capers, and Worcestershire sauce and process until smooth. Add the olive oil and anchovy oil and process until emulsified. You should have about 1 cup. You will need only 1/2 cup for this recipe. The leftover dressing will keep in an airtight container in the refrigerator for up to 3 days.
To prepare the greens and celery root:
- Trim off the stems from the dandelion greens, then cut the greens into 2-inch pieces. Trim the frisée, discarding the green tops and stems. Cut the pale yellow leaves that remain into 2-inch pieces. Rinse and dry the dandelion and frisée well.
- Cut away the core of the radicchio, then cut the radicchio lengthwise into sixths. Peel the celery root and cut in half lengthwise. Using a mandoline, shave each half crosswise into thin slices.
To make the grilled cheese croutons:
- Line up the bread slices on a work surface and spread the slices evenly with the butter. Turn 2 slices butter side down, then divide the cheese slices evenly between the 2 slices.
- Top with the remaining 2 bread slices, butter side up. Heat a large nonstick skillet over medium heat. Add the sandwiches and toast, turning once, for 5 to 10 minutes, until the cheese melts and the bread is browned and crisp.
- Transfer the sandwiches to a cutting board, let rest for 2 to 3 minutes, and cut into 1/2-inch squares.
To assemble the salad:
- In a large bowl, combine the greens and celery root. Drizzle with 1/2 cup of the vinaigrette, season with salt and a generous amount of pepper, and toss to coat evenly. Scatter the croutons over the top, toss again, and serve immediately.