Preheat a grill or grill pan over medium heat.
Season the chicken breast with salt and pepper on both sides and drizzle with oil.
Grill the chicken on each side to an internal temperature of 160°F (71°C).
Remove the chicken from the grill and let it rest for a few minutes before slicing it thinly.
Bring a large pot of salted water to a boil. Cook the ravioli according to package directions until al dente. Reserve 1/2 cup of the pasta cooking water or more for more than 2 servings. Drain the ravioli.
Meanwhile, heat the olive oil in a large skillet over high heat. When the oil shimmers, add the shallots and cook until fragrant, 2 - 3 minutes. Add the mushrooms and season with salt and pepper. Cook undisturbed for 5 minutes or until golden, stir, and continue cooking until the mushrooms have caramelized, 3 - 5 minutes. Reduce the heat to medium. Add the butter, garlic, thyme, and sage. Cook, stirring occasionally until the garlic is caramelized and fragrant, about 5 minutes.
Add the balsamic and a splash (about 1/4 cup) of the pasta cooking water. Cook for 2 minutes. Remove from the heat and discard the garlic cloves.
Bring a pot of salted water to a boil. Add the green beans and blanch them for 2 - 3 minutes until they are bright green and slightly tender. Drain and set aside.
In a large skillet, heat the extra-virgin olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant but not browned.
Add the blanched green beans to the skillet. Sauté for another 2 - 3 minutes, tossing occasionally, until the beans are tender-crisp.
Season the green beans with salt and pepper to taste. Remove from heat.
Mix the ingredients for the spritzer. Serve over ice if desired.
Serve the ravioli with mushroom sauce and grilled chicken. Enjoy with green beans and peach spritzer!