In a small bowl, whisk the vinegar, shallot, mustard, salt, and a few grinds of pepper. Let the mixture stand for 10 min. and then whisk in the olive oil. Add 2 Tbs. of the crumbled blue cheese and stir gently.
Remove any tough, discolored, or broken outer leaves from the escarole. Trim off the root end with a sharp knife. Tear the leaves into bite-size pieces, wash well, and spin dry thoroughly (you should have about 6 lightly packed cups). Store in a large serving bowl covered with a slightly damp towel in the refrigerator until ready to toss. (If storing for more than an hour, cover the towel-covered bowl with plastic wrap to prevent the towel from drying out.)
Up to 1 hour before serving the salad, peel, core, and dice the apple into 1/4-inch cubes (you should have about 1-1/4 cups). Reserve the apple in a medium bowl. Slice the thick skin from the celery root and dice it the same size as the apple (you should have about 1-1/2 cups). Add the celery root to the diced apple and toss with 2 Tbs. of the vinaigrette to prevent discoloration. Cover and refrigerate until ready to toss the salad.
Toss the escarole and the apple and celery root mixture with the remaining dressing. Break up the pecans into the salad and toss again to incorporate. Season to taste with salt and pepper. (The blue cheese will add a little saltiness, so take care not to oversalt the salad.) Crumble the remaining blue cheese over the salad just before serving.
The vinaigrette tastes best when made ahead, so prepare it up to two days before serving and store it in the refrigerator, tightly covered. Bring the vinaigrette to room temperature and whisk lightly before dressing the salad.