Heat 1 tablespoon of the oil in a medium saucepan over medium heat. Add the shallots and a pinch of salt, and cook, stirring occasionally, until lightly browned, 6 to 8 minutes. Add the garlic and chopped jalapenos, and cook, stirring occasionally, until the garlic is soft, about 2 minutes. Add the cranberries, sugar, 3/4 cup water and jalapeno brine. Bring to a boil, then reduce to a simmer and cook until the cranberries have all burst, 8 to 10 minutes. Transfer to the bowl of a food processor, and process until completely smooth. Season to taste with additional salt if needed. Pour into a serving dish, and cover with plastic wrap so it does not form a skin while you fry the chicken wings.
Fill a large Dutch oven halfway with oil, and heat to 375 degrees F.
Toss half the chicken wings with a large pinch of salt in a large bowl. Put the cornstarch and 1/2 teaspoon salt in another large bowl. Add the wings to the cornstarch, and toss to completely coat. Shake off the excess cornstarch, and fry the chicken wings in the hot oil until light golden brown and cooked through, 10 to 12 minutes, turning occasionally. (It's OK if the temperature drops slightly, though not below 350 degrees F, as the chicken wings fry.) Transfer the fried wings to a paper towel-lined baking sheet to absorb any excess oil. Sprinkle liberally with salt. Let the oil return to 375 degrees F, then season, dredge and fry the remaining wings.
Garnish the dipping sauce with the sliced pickled jalapenos, and serve alongside the hot chicken wings. The sauce can be made a day ahead, refrigerated and rewarmed before serving; if it thickens overnight, thin it out with 1 to 2 tablespoons water.
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