Heat the oil in a Dutch oven set over medium heat and add the butter.
2 tablespoons olive oil, 2 tablespoons unsalted butter
Lightly season the chicken with kosher salt and black pepper, and add it to the pot. Cook just until chicken is no longer pink on the inside and transfer it to a paper towel-lined plate; set aside.
2½ pounds boneless, skinless chicken thighs, 2 teaspoons kosher salt, ½ teaspoon freshly ground black pepper
If needed, add a little more oil and butter to the pot and sauté the chopped carrots and celery, about 2 minutes, or until a fork inserted in a carrot still has a little resistance.
2 carrots, 1 rib celery
Add the chopped onion and apple and cook for about 4 minutes, stirring occasionally, or until the onions are translucent and the apples have softened.
1 yellow onion, 1 Granny Smith apple
Add the chopped garlic and cook for about 30 seconds, or until the garlic is fragrant and has bloomed.
3 cloves garlic
Add the curry powder, garam masala, cumin, red pepper flakes, and ginger.
2 tablespoons sweet curry powder, 1 tablespoon garam masala, 1 teaspoon ground cumin, ½ teaspoon crushed red pepper flakes, 1 (1-inch piece) fresh ginger
Add the coconut milk, broth, tomato paste, and rice. Stir well and heat to a low boil. Reduce the heat to low and add the chicken.
14.5 ounces coconut milk, 4 cups unsalted chicken broth, 1 tablespoon tomato paste, ½ cup dry white rice
Simmer, stirring often, until the rice is cooked through and soup has thickened to desired consistency, about 30-45 minutes. Taste the soup periodically and adjust the seasonings, if needed.
While the soup simmers, make the buttered crackers: combine all ingredients in a small bowl and mix together until uniform.
1 sleeve Ritz crackers, 2 tablespoons unsalted butter, ¼ teaspoon fine sea salt, ¼ teaspoon sweet curry powder
Garnish bowls of soup with the buttered crackers, yogurt, cilantro, and/or sliced scallions.