In a medium saucepan, bring 1 1/2 cups water to a boil. Add the basmati rice, reduce heat to low, cover, and simmer for 15 minutes or until tender. Remove from heat and let stand, covered, for 5 minutes. Fluff with a fork and set aside.

Season the chicken pieces with 1 teaspoon salt and 1/2 teaspoon pepper. Heat the olive oil in a large Dutch oven or heavy pot over medium heat. Add the chicken and shallot, and cook, stirring occasionally, until the chicken is golden brown on all sides, about 6 to 8 minutes.

Stir in the tomato paste, red curry paste, minced garlic, and grated ginger. Cook, stirring constantly, until very fragrant, about 2 minutes.

Pour in the coconut milk and chicken stock, and stir to combine. Season with a pinch of salt and pepper. Bring the mixture to a gentle boil, then reduce the heat to low and let it simmer until the sauce thickens slightly, about 7 to 10 minutes.

Add the sliced red and yellow bell peppers and the peach chunks to the pot. Continue to simmer until the peppers are tender-crisp, about 5 to 8 minutes.

Remove the pot from the heat. Stir in the chopped cilantro, Thai basil, and fresh lime juice. Taste and adjust seasoning with more salt or pepper if needed. Serve the curry over the cooked rice.