Start by patting the chicken thighs dry with paper towels. Season both sides generously with kosher salt.
In a large Dutch oven, heat 2 tablespoons of olive oil over medium-high heat. Add the chicken thighs, skin-side down. Sear for about 5-7 minutes until the skin is golden brown and crispy. Flip and cook for an additional 5 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the thinly sliced garlic and anchovies. Cook, stirring frequently, for about 2 minutes until the garlic is fragrant and the anchovies have melted into the oil.
Add the crushed red pepper flakes and tomato paste to the pot, stirring to combine. Cook for another minute to deepen the flavor. Then, pour in the diced tomatoes, olives, capers, and chicken broth. Stir well to incorporate all the ingredients.
Nestle the seared chicken thighs back into the pot, skin-side up. Add the bay leaves on top. Bring the mixture to a simmer, then reduce the heat to low. Cover and let it cook for about 30 minutes.
After 30 minutes, remove the lid and check the chicken for doneness; it should reach an internal temperature of 165°F. If needed, simmer uncovered for an additional 5-10 minutes to thicken the sauce. Remove the bay leaves before serving.