Heat olive oil in a pot over medium heat and sauté onion, garlic, carrot, and bell pepper until softened, about 3 to 4 minutes.
Add paprika, allspice, thyme, turmeric, cumin, salt, and pepper, cooking for 30 seconds until the spices are fragrant.
Stir in the rinsed rice and kidney beans, coating them well with the spices.
Pour in coconut milk, vegetable broth, and soy sauce; stir and bring to a gentle boil.
Cover the pot, reduce heat to low, and simmer for 15 to 18 minutes until the rice is tender and the liquid is absorbed.
Fold in chopped spinach and lime juice, cover, and let wilt for 2 minutes.
Fluff the pelau with a fork and serve warm.