Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
For the chicken and vegetable base: Heat a 12-inch cast-iron skillet over direct heat. Melt the butter. Add the carrots, onions and thyme. Season with salt and pepper and cook until the vegetables begin to soften, 3 to 5 minutes. Stir in the flour, coating the vegetables, and continue to cook for another minute. Whisk in the chicken stock, smoothing out any flour lumps. Simmer until the mixture begins to thicken, 10 to 15 minutes.
Meanwhile, make the dumplings: Melt the butter with the jalapeno if using and lime juice in a sauce pot over indirect heat, then let cool.
Whisk together the flour, baking powder, celery seeds, salt and lime zest in a large bowl. Mix in the cheese.
Slowly pour the melted butter mixture into the cold cream in a small bowl and mix together using a fork. (The butter will bead up as you mix.) Pour the butter-cream mixture into the flour mixture and bring together into a soft dough. Set aside.
Finish the chicken and vegetable base: Add the chicken, peas and parsley to the skillet with the vegetables. Move the skillet over indirect heat and scoop the biscuit mixture on top, covering the surface of the pan. Cover the grill and cook until the biscuits are golden brown and cooked through, about 20 minutes.
(Alternatively, you can make the sauce and melt the butter mixture on a stovetop, then bake the biscuits in a 375 degrees F oven for 15 to 20 minutes.)
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