Preheat oven to 450°F. Line a large baking sheet with parchment paper.
Mix the balsamic vinegar and honey in a small saucepan. Bring to a boil over medium heat then reduce heat to simmer, stirring occasionally. Cook for 15-20 minutes or until glaze has thickened enough to coat the back of a spoon. Remove from heat. Let cool for 5 minutes.
Add remaining glaze ingredients to the balsamic mixture. Mix until well combined. Set aside about one-fourth of the glaze in a separate bowl to add after cooking.
Season salmon well with salt and pepper. Place salmon skin-side down on prepared baking sheet and generously brush the flesh side with the balsamic glaze.
Place the salmon in the oven and bake until salmon flakes nicely. Baking time will depend on the thickness of the thickest part of the filet. For every inch of thickness, bake 8 to 10 minutes.
Remove from oven and use a clean utensil to brush the glaze set aside earlier onto the cooked salmon. Top with fresh parsley and dill and serve.