Combine the first 5 ingredients in a small bowl to make the Seasoning Mix.
Sprinkle the chicken evenly with 1 tablespoon plus 1 teaspoon of the Seasoning Mix and rub it in well.
Heat the oil in a heavy 4-quart pot over high heat just until it begins to smoke, about 3-4 minutes. To the pot add the chicken, large pieces first and skin sides down, and cook, turning frequently, until golden brown on both sides, about 10 minutes per batch.
Remove the chicken from the pot and set it aside.
To the pot add the onions, jalapeño peppers, and the remaining seasoning mix. Cook, stirring and scraping the pot every 2 or 3 minutes, until the vegetables begin to brown, about 7 minutes. Even the jalapeño peppers will have a tinge of slightly sweet flavor, believe it or not! Add the flour and stir until the white is no longer visible. Spread the mixture evenly over the bottom of the pot and cook until a brown crust forms, about 2-3 minutes. Scrape up the crust, which should be a pretty light brown with a reddish tinge and will be very sweet and flavorful, then add the stock and stir until the crust dissolves. Reduce the heat to medium-low, add the cream and two cheeses, and return the chicken and the accumulated juices to the pot. Cook, stirring every 3 or 4 minutes, until all the cheese melts (taste the incredible richness now!), about 10 minutes. Add the sugar snap peas and simmer until they are just cooked, but still sweet and crunchy, about 12 minutes. Serve on a mound of your favorite pasta or rice.