Preheat oven to 400°F (rack in the middle).
Soften 8 oz cream cheese (leave at room temperature about 15–30 minutes or microwave in 5–10 second bursts until spreadable). In a bowl, combine the softened cream cheese, the 2 pressed garlic cloves, and 1/4 cup green onions (finely chopped). Stir until evenly mixed. Divide the filling into four equal portions.
Pat 4 chicken breasts dry with paper towels. With a sharp knife, cut a horizontal slit through the thickest side of each breast to make a pocket, being careful not to cut all the way through.
Stuff each chicken breast with one quarter of the cream cheese mixture. Close the pocket and secure with a toothpick if needed.
Pour the 1/4 cup everything but the bagel seasoning into a shallow dish or plate. Roll and press each stuffed chicken breast in the seasoning so all sides are coated. Arrange the breasts on a baking sheet or in a casserole dish, seam-side down.
Bake at 400°F for 20–30 minutes, until the internal temperature of the chicken reaches 165°F when measured in the thickest part of the breast.
Remove from the oven, discard toothpicks, and let the chicken rest 3–5 minutes before serving.