Trim the sprouts by cutting the very base off each one, then peel away any tired outer leaves. Put them on a board, slice them thinly, then transfer to a large bowl.
Add the apple slices and celeriac matchsticks, squeeze over the lemon juice and season.
Combine all the dressing ingredients and stir well.
Trickle half the dressing over the slaw ingredients and toss together. Pile the slaw on to a serving plate, spoon over the remaining dressing and finish with a scattering of tarragon leaves.