Heat a bbq up to high heat. Be sure the grill is very hot for apricots to grill without cooking through.
Make balsamic glaze by combining balsamic vinegar and chosen sweetener in a small saucepan. Bring mixture to a low simmer over medium heat. Cook for 10-15 minutes until mixture has reduced by half, and is sweet and lost it's acidic bite. If you accidentally over-reduce the mixture, add water 1 tablespoon at a time until the mixture is a good consistency for drizzling.
In a small dish, mix together olive oil and honey, and stir to combine.
Cut or break the tough ends off the bottom of the asparagus, and cut the apricots into halves.
Use a brush to coat asparagus and halved apricots with honey-olive oil mixture.
Season lightly with sea salt and black pepper.
Grill the asparagus and apricots. Place apricots on high heat area of grill. Only lightly grill the outside, 2-3 minutes total, to prevent apricots from cooking through and becoming too mushy.
When the asparagus is grilled to your liking, and apricots are grilled, remove from heat.
Drizzle balsamic glaze and garnish with walnuts.