Grab a cast iron skillet and set it over medium heat. Drizzle in a little olive oil, then toss in the onion & pepper. Cook, stirring every so often, until it turns soft and golden, about 10 minutes.
Build the flavor base: Add in the chili powder, paprika, thyme, cayenne, and a pinch of salt and pepper. Let that cook down another minute or so — it should smell amazing at this point.
Add the good stuff: Pour in your beer and give everything a good stir to deglaze the bottom. Add the chicken, sausage, diced tomatoes, and green chilies. Stir to combine, cover, and let it all gently simmer for about 25–30 minutes, until the chicken is tender and easy to shred. Preheat your oven to 375°F.
Shred and thicken: Once the chicken’s ready, shred it right in the pot using two forks. In a small bowl, whisk together the heavy cream and cornstarch, then stir that into the pot. Let it simmer for another 5 minutes to thicken into a creamy, rich sauce.
Make the biscuit topping: In a separate bowl, mix together the flour and baking powder. Add the grated butter and toss until crumbly. Stir in the honey, beer, and cheddar cheese just until combined — don’t overmix; rustic is good here.
Assemble and bake: Drop spoonfuls of the biscuit dough evenly over the top. Pop the whole thing in the oven and bake for 15–20 minutes, until the biscuits are golden and puffed and the filling is bubbling around the edges.
Cool and serve: Let it rest for about 5 minutes before digging in — the sauce will thicken up slightly as it cools. Then grab a spoon and go to town.