Preheat the oven to 425°F (220°C).
In a medium mixing bowl, combine the crumbled goat cheese, chopped basil, toasted chopped walnuts, thyme leaves, a pinch of kosher salt, black pepper, and crushed red pepper flakes; mix until evenly distributed.
Season each chicken breast with salt and pepper. Using a sharp knife, slice horizontally through the thickest part of each breast to create a pocket, cutting almost to the other side but leaving about 1/2 inch attached.
Open each chicken breast like a book and spread an even portion of the goat cheese mixture onto one side of the pocket. Drizzle about 1/2 tablespoon of honey over the filling for each breast, then close to enclose the filling; some filling may peek out and that’s fine.
Heat the extra virgin olive oil in a large ovenproof skillet over medium-high heat until shimmering. Add the stuffed chicken and sear until golden, about 3–5 minutes per side. Remove the chicken to a plate, leaving any browned bits in the pan.
Reduce heat to medium and add the butter, then stir in the minced garlic and dry orzo. Cook, stirring, until the garlic is fragrant and the orzo is lightly toasted, about 2–3 minutes.
Add the chicken broth, torn kale, and balsamic vinegar to the skillet. Stir to combine and bring the mixture to a boil.
Slide the seared stuffed chicken 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 for 2–3 minutes, then serve the chicken over the orzo and kale, topped with additional fresh basil.