Gather all ingredients and prepare your mise en place. In a large pot or Dutch oven over medium heat, melt the Kerrygold butter until foamy. Once melted, add the flour and stir constantly for 2 minutes to create a roux, which will thicken the chili and give it a rich, slightly nutty flavor. You want the roux to turn a light golden color but not brown—this is your flavor foundation.
Slowly whisk in the chicken broth and half-and-half to the roux, stirring constantly to avoid lumps. Once fully incorporated, increase the heat to medium-high and bring to a boil. Let it boil for about 2 minutes, stirring occasionally, until the mixture thickens noticeably. This creates a velvety base that will coat all the other ingredients beautifully.
Reduce heat to medium-low. Add the shredded rotisserie chicken, crumbled bacon, rinsed white kidney beans, diced jalapeños, onion flakes, garlic powder, cumin, chili powder, smoked paprika, salt, and black pepper to the pot. Stir well to combine everything evenly. I like to add the jalapeños early so their flavor infuses throughout the chili rather than just sitting on top—this gives you heat and flavor in every spoonful.
Let the chili simmer gently for 10-15 minutes, stirring occasionally, so the flavors meld together and the jalapeños soften slightly. Add the softened cream cheese cubes and stir until completely melted and incorporated, creating an incredibly creamy and rich texture. Finish with a squeeze of fresh lime juice, which brightens the heavy cream and adds a subtle tang that makes the jalapeño flavors pop.