Preheat the oven to 425°F (220°C).
In a bowl, combine the crumbled goat cheese, chopped basil, toasted chopped walnuts, thyme, a pinch of salt, black pepper, and crushed red pepper flakes; mix until evenly combined.
Season each chicken breast with salt and pepper. Carefully slice each breast horizontally almost through, leaving about 1/2 inch uncut so it opens like a book.
Divide the goat cheese mixture among the chicken breasts, spreading it on one side of each. Drizzle about 1/2 tablespoon of honey over the filling in each breast, then fold the chicken closed to enclose the filling.
Heat the olive oil in a large oven-safe skillet over medium-high heat until shimmering. Sear the stuffed chicken breasts 3–5 minutes per side, until golden brown. Remove the chicken from the skillet and set aside.
Reduce heat to medium. In the same skillet, add the butter, then the minced garlic and 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 and stir to combine. Bring the mixture to a boil.
Slide the seared chicken breasts and any accumulated juices back into the skillet on top of the orzo mixture. Transfer the skillet to the preheated oven and roast until the chicken is cooked through, 10–15 minutes.
Remove from the oven, let rest for a couple minutes, then serve the chicken topped with additional fresh basil.
