In a large mixing bowl combine the bulgar wheat, lemon zest, 1/2 teaspoon of salt and 1/4 teaspoon of pepper with 1 1/2 cups of boiling water in a bowl. Wrap tightly with plastic and set aside for about an hour.
In a medium sauce pan, over medium heat, sweat the shallot with 2 tablespoons of oil and a good pinch of salt and pepper for about 3-4 minutes Add the garlic and soften for about 1-2 minutes.
Add the apple and juice from half of your lemon. Cook for 1-2 minutes and then turn off the heat, leaving the pan on the burner. The goal is to warm the apple through, keeping the integrity of the texture. You don’t want then to get mushy. Mix in 1/2 of thyme and let the pan cool.
Fluff the bulgar with a fork. In a small bowl whisk the juice of the other half of the lemon (about 2 tablespoons), and 3 tablespoons of the oil, remaining thyme, 1/4 teaspoon each of salt and pepper. Mix thoroughly to combine. Pour over the bulgar and toss.
Add in the cooled apple mixture and toss gently. Taste for seasoning. Add the nuts and arugula and toss gently. Serve at room temperature over additional arugula, if desired.