Mix the ground pepper, cumin, coriander, turmeric, and salt in a small bowl and set the spice blend aside.
Heat the olive oil and butter in a large pot or Dutch oven over medium heat until the butter melts.
Add the minced garlic, minced ginger, and chopped onion and cook, stirring, for about 1 minute until fragrant.
Add the reserved spice blend and stir to coat the aromatics, cooking about 30 seconds to bloom the spices.
Add the cubed chicken breasts and cook, stirring occasionally, until the pieces are no longer pink on the outside, about 4–5 minutes.
Pour in the can of coconut milk and the chicken broth; the liquid should mostly cover the chicken—add a bit more broth if needed.
Drain the baby corn and green beans, cut the baby corn into halves or thirds if desired, and add both to the pot. Stir to combine.
Whisk the cornstarch with a few tablespoons of the hot broth taken from the pot until smooth, then stir the slurry back into the pot to thicken the sauce.
Cover the pot and simmer gently for 20–30 minutes, until the chicken is cooked through and flavors have melded.
Adjust seasoning if needed and serve warm.