Preheat the oven to 375 degrees F.
Heat a medium pot (preferably oven safe) over medium heat and add the olive oil. Add the onion and cook, stirring often, until softened, 10 minutes. Add the bell pepper, chili powder, paprika, thyme and cayenne and season with salt + pepper and cook another 5 minutes. Pour in the beer. Add the chicken, sausage, tomatoes and green chilies, stirring to combine. Bring to a simmer, cover and simmer 25-30 minutes or until the chicken is cooked through and shreds easily. Shred the chicken with two forks, leave to simmer.
Whisk together the heavy cream and cornstarch and stir into the chicken. Simmer 5 minutes and then remove from the heat.
Meanwhile, combine the flour, baking powder and butter in a medium bowl and toss to combine. Add the honey and beer and mix until just combined. Fold in the cheddar.
Remove the chicken from the heat. If not already in an oven safe dish, then transfer to one. Drop 2 tablespoons of biscuit dough over top the chicken. Place in the oven and bake for 15-20 minutes or until the biscuits are golden. Remove from the oven and let cool 5 minutes. Eat!