Warm the oil in a large Dutch oven over medium heat. Add the chicken thighs, season with 1 teaspoon of salt, and cook for 8-10 minutes, turning once, until cooked through. Remove the chicken and, once cool enough to handle, chop or shred it into bite-sized pieces.

Reduce the heat under the Dutch oven. Add the garlic, shallot, jalapeño or serrano pepper, and red bell pepper to the same pan. Cook until the vegetables soften and become fragrant while scraping up the browned bits from the bottom without burning the garlic.

Add the tomato paste, cumin, allspice, thyme, and remaining 1 teaspoon salt. Cook for 2-3 minutes until the tomato paste deepens in color.

Preheat the oven to 350°F (177°C). Add the beer to the Dutch oven, simmer for a few minutes to reduce, then add the crushed tomatoes, chicken broth, and bay leaf. Bring the mixture to a low simmer.

Stir the chicken and uncooked rice into the simmering mixture. Bring back to a low simmer, cover with the lid, and bake for 30 minutes.

Remove the lid and fluff the rice with a fork. Stir in the green olives, cilantro, and lime juice, then adjust seasoning to taste before serving.