To the bowl with the reserved, chopped pieces of pepper, add the ground chicken, rice, thyme, 1 tablespoon cumin, tomatoes, a couple handfuls of cilantro, scallions, lime juice and some salt and freshly ground black pepper. With your hands or a spoon (hands will be faster), combine all the ingredients thoroughly.
Using a spoon or your hands, stuff each of the 6 pepper boats with the chicken mixture. Once they're filled, arrange the peppers in a casserole pan, alternating stem end and bottom end so that they all fit snugly in the pan. Add a splash of water or chicken stock to the pan and cover with tin foil. Transfer the pan to the oven along with the foil-wrapped garlic head and bake 45-50 minutes. Remove foil and cook an additional 5-10 minutes, until nicely brown and cooked through.
About 10 or 15 minutes before the peppers and garlic come out of the oven, make the cheese sauce: Melt the butter in a medium-size saucepot over medium-high heat. Add the flour and cook for one minute. Whisk in 1 cup of chicken stock and the milk, and bring up to a bubble. Cook until thickened. Season with some salt and pepper, turn the heat down to low and stir in the cheese until melted. Reserve until ready to serve. (If it thickens up too much as it sits, whisk in a splash of chicken stock to loosen.)
For the beans, place another medium-size saucepot over medium heat with one turn of the pan EVOO. Add the onions, remaining teaspoon of cumin and cook, stirring every now and then for 3-4 minutes. Add the drained black beans and remaining 1/2 cup of chicken stock and cook to warm through.
Remove the peppers and the garlic from the oven and let the peppers rest while you finish up the black beans: If the garlic is too hot to handle, fold over a couple of pieces of paper towel, place the stem end of the garlic in the center and use the paper towel as a finger barrier as you squeeze out the roasted flesh onto a cutting board. Once all the cloves are out, smash them up with the side of a knife then add the paste to the heated beans. Season with some salt, freshly ground black pepper and some hot sauce, and stir to combine.
To serve, cover the bottom of four serving plates with some of the cheese sauce, then place two of the roasted peppers in the middle of the plate. Top with some of the chopped green olives and reserved cilantro, and serve the beans alongside.