Preheat oven to 400°. Line a rimmed baking sheet with foil.
For pork: In a small bowl, stir together olive oil, dill, mint, parsley, salt, pepper, and garlic; rub mixture all over pork. Place on prepared pan.
Bake until a meat thermometer inserted in thickest portion registers 145°, 30 to 35 minutes. Let stand for 10 minutes before slicing.
Meanwhile, for sauce: In a small saucepan, melt butter over medium-high heat. Add garlic; cook, stirring frequently, until tender, about 30 seconds. Stir in vinegar, and bring to a boil. Reduce heat, and simmer until liquid is reduced by half, about 5 minutes. Stir in chicken broth, and bring to a boil.
In a small bowl, whisk together cornstarch and 1 tablespoon water until dissolved. Whisk cornstarch mixture into broth mixture, and cook, whisking constantly, until thickened, about 1 minute. Whisk in honey and salt. Serve warm with pork.
Notes
Make-Ahead Tip: The herb mixture can be rubbed onto the pork and refrigerated up to a day ahead. Let the pork stand at room temperature for 30 to 45 minutes before you cook it.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/herb-roasted-pork-loin-with-balsamic-sauce-recipe/