Step 1

Preheat oven to 350°. Toast walnuts on a rimmed baking sheet, tossing once, until golden brown, 5–8 minutes; let cool.

Step 2

Finely chop 1 shallot half, then thinly slice the other half crosswise; set sliced shallot aside. Combine chopped shallot, mustard, sugar, and ¼ cup vinegar in a resealable jar. Add oil and season with salt and pepper. Cover and shake to emulsify; set vinaigrette aside.

Step 3

Toss figs, reserved sliced shallot, and remaining ¼ cup vinegar in a small bowl; let sit until figs and shallots are softened, at least 30 minutes.

Step 4

Just before serving, toss fennel, celery, blue cheese, and toasted walnuts in a large bowl. Drain figs and shallot and add to bowl. Drizzle with vinaigrette and toss to coat; season with salt and pepper.

Step 5

Do Ahead: Vinaigrette can be made 1 day ahead; cover and chill. Figs and shallot can be soaked 4 hours ahead; store covered at room temperature. Fennel and celery can be sliced 4 hours ahead; place in a large bowl. Cover with a damp paper towel and chill.