Preheat oven to 375°. Wipe dirt off mushrooms, trim tough stems, and cut large mushrooms to make all pieces about the same size. Toss in a bowl with 1/4 cup oil, 1/2 tsp. salt, and the pepper. Spread on a rimmed baking sheet. Bake, stirring occasionally, until browned, 30 to 45 minutes. Let cool.
Make dressing: Sprinkle peeled garlic clove with remaining 1/4 tsp. salt, mince, and then flatten with side of chef's knife into a paste. Scrape paste into a jar with a tight-fitting lid and add mustard, honey, thyme, vinegar, and remaining 1/4 cup oil. Cap jar and shake until emulsified.
Peel celery root, then cut into matchsticks, dropping them into a bowl of water to prevent darkening. Pat dry, then put in a large salad bowl and add chicories and mushrooms. Toss gently with dressing.
Make ahead: Dressing, up to 1 day ahead, chilled. Prep vegetables 1 day ahead (chill celery root matchsticks in water), then dress just before serving.
Note: Nutritional analysis is per serving.