Prep the ingredients: finely chop the onion; dice the carrot and celery; peel, core, and dice the apple; mince the garlic; grate the ginger; rinse the rice until the water runs clear.
Heat the vegetable oil in a large pot over medium-high heat. Add the chicken thighs and cook, stirring occasionally, until lightly browned on the edges, 5–7 minutes. Transfer the chicken to a bowl.
Reduce heat to medium. Add the onion, carrot, celery, and apple to the pot and cook, stirring, until the onion is translucent and the vegetables soften, 6–8 minutes.
Add the garlic and ginger and cook until fragrant, about 1 minute.
Stir in the curry powder and tomato paste and cook, stirring constantly, until the spices smell toasty and the paste darkens slightly, 1 minute.
Return the chicken to the pot. Add the basmati rice, chicken stock, bay leaf, kosher salt, and black pepper. Bring to a boil, then reduce to a gentle simmer.
Simmer uncovered, stirring occasionally, until the rice is tender and the soup has thickened slightly, 20–25 minutes. Doneness cue: rice should be soft but not blown out, and chicken cooked through.
Remove and discard the bay leaf. Stir in the lemon juice and adjust seasoning to taste.
Ladle into bowls and top with cilantro leaves; serve with lemon wedges.