Preheat the oven to 425°F (220°C).
In a medium bowl, combine the crumbled goat cheese, chopped basil, toasted walnuts, thyme, a pinch of kosher salt, black pepper, and crushed red pepper flakes; mix until evenly combined.
Season each chicken breast with salt and pepper. Slice each breast horizontally nearly through, leaving about 1/2-inch attached so it opens like a book.
Spread the goat cheese mixture evenly over one side of each opened chicken breast and drizzle about 1/2 tablespoon of honey over the cheese on each breast. Fold the chicken closed to enclose the filling.
Heat the olive oil in a large ovenproof skillet over medium-high heat. When the oil shimmers, sear the stuffed chicken breasts until golden, about 3–5 minutes per side. Remove the chicken to a plate, keeping any juices and stray cheese.
Reduce heat to medium and add the butter to the same skillet. Stir in the minced garlic and the orzo; cook, stirring, until the garlic is fragrant and the orzo is lightly toasted, about 2–3 minutes.
Pour in the chicken broth and balsamic vinegar, then add the torn kale. Bring the mixture to a boil and stir to combine.
Slide the seared chicken breasts and any accumulated juices back into the skillet on top of the orzo. Transfer the skillet to the preheated oven and roast until the chicken is cooked through and the orzo is tender, about 10–15 minutes.
Remove from the oven, let rest a few minutes, then serve the chicken topped with additional fresh basil.