Preheat the oven to gas 2, 150°C, fan 130°C. Mix the nuts with the cayenne and 1tsp of the honey, then spread over a baking sheet and bake for 15 minutes, until toasted. Cool. Whisk the remaining honey with the dressing ingredients and season to taste. The nuts and dressing can be made two days ahead and kept chilled until you're ready to use them.
Half-fill a large bowl with cold water and add the lemon juice and sliced apples. Peel the celeriac and cut into thin slices, then stack together and slice into matchsticks. Add to the bowl. Prepare the beetroot the same way and place in another bowl.
To serve, thoroughly drain the celeriac and apple. Mix them with the beetroot, dressing and the spring onions, then scatter the candied nuts over the top.