Combine 8 cups water, the salt, sugar, pickling spice, garlic, thyme, ginger and lemon and in a large pot. Add the chicken and refrigerate 3 to 4 hours, or overnight.
Remove the chicken from the brine, place on a rack set over a plate to air dry the chicken (the skin turns yellow and dry and makes it crispier). It's really important to air dry the skin as much as possible or you won't get a good sear on the chicken; the skin will be too soft and filled with water. To do this, put the brined chicken skin-side up over a plate covered with paper towels and lay in the fridge for another day.
For the pepper and tasso stew:
Add the stock, ham, chile peppers, bells peppers and tomato to a shallow saute pan and reduce by half, but not too much, because we'll cook it some more later with the chicken.
For the polenta:
Bring the cream and 4 cups water to boil. Whisk in the cornmeal, then turn down the heat to low and let it cook, whisking every couple minutes, about 30 minutes to cook completely. When it's almost done, whisk in the cheese and season with salt and pepper. Keep warm.
Preheat the oven to 400 degrees F. To bring together, heat up a large fry pan and add the oil for frying. When it first smokes, add the chicken skin-side down and sear on medium-high heat until the skin is starting to crisp but otherwise the chicken is still raw. Flip the chicken over and place on the reduced pepper stew and put it in the oven (with the fan on if you've got one) and let it stew for another 12 minutes or so, until the chicken plumps up a bit and feels firm to the touch. Thermometer should read 165 degrees F.
Then when it's all done, lump down some of that creamy, cheesy polenta, move the chicken to the side a little bit and load some pepper and tasso stew down onto the plate. Top with the crispy brined chicken.