Cook the onion and black pepper over medium heat in the vegetable oil in a 3-quart pot until the onion is a little yellow, then add the garlic, stirring frequently, until both are golden and softened (total of about five minutes or so).
Add curry powder and cook for another two minutes, stirring frequently (very important, as the curry powder will clump up and burn if you don't).
Add the can of petite diced tomatoes (no draining!), as well as the broth, and simmer uncovered for about five minutes.
Mix the hot water and peanut butter together until smooth, then add to the pot. Toss the shredded chicken and cilantro in, too.
Simmer, uncovered and stirring occasionally, for another five minute or so.