Whisk together the peanut butter, chicken broth, soy sauce, honey, minced garlic, and hot sauce in a medium bowl until smooth. Set aside.

Heat 2 tablespoons peanut oil in a large skillet over medium-high heat. Add the broccoli and julienned carrots. Cook, stirring frequently, for 3 to 6 minutes until the broccoli turns bright green and is just beginning to turn tender. Add the sliced red bell pepper and cook for 1 to 2 more minutes. Remove vegetables and set aside.

Cut the chicken into 2-inch pieces and pat completely dry with paper towels. Season with white pepper, salt, and paprika. Add the cornstarch and toss until each piece is evenly coated.

Heat 1/3 cup peanut oil in the same skillet over medium-high heat. Fry the chicken in batches, leaving space between each piece. Flip once the bottom is light golden brown and crisp, about 3 to 4 minutes per side. Do not crowd the pan. Set cooked batches aside.

Wipe excess oil from the skillet with a paper towel held with tongs. Return all the cooked chicken to the pan. Whisk the peanut sauce to recombine, then pour it over the chicken. Toss to coat. Reduce heat to medium and let the sauce heat through and thicken naturally, about 1 to 2 minutes. Add a splash of water if the sauce gets too thick.

Add the stir-fried vegetables back to the skillet or plate on the side. Garnish with sliced green onions and chopped peanuts. Serve hot over white rice or noodles.