Combine chicken, cornstarch, and 2 teaspoons fish sauce in a medium bowl. Allow to marinate 20 minutes.
Heat a large skillet or wok over medium-high heat. Add 1 tablespoon vegetable oil and swirl to coat bottom. Add chicken in a single layer and sauté 3-5 minutes, tossing frequently until chicken is cooked through.
Add remaining 1 tablespoon vegetable oil to same pan and swirl to coat bottom. Add onion, sweet pepper, green beans, and bamboo shoots to pan and sauté over medium-high heat 3-5 minutes until vegetables are crisp-tender. Add garlic, ginger, and curry paste to vegetables and cook 1-2 additional minutes until fragrant.
Add coconut milk, chicken broth, seared chicken, and remaining 2 teaspoons fish sauce to pan. Season curry with salt and pepper to taste and bring to a simmer over medium-high heat. Reduce heat to medium-low and allow curry to simmer uncovered 10-15 minutes, stirring occasionally.
Remove curry from heat and fold in basil and spinach until wilted. Season curry with additional salt and pepper to taste if needed. Serve curry warm over steamed jasmine rice with fresh cilantro and a few sprinkles of lime zest. Enjoy!