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Place the chicken in a slow cooker. In a large bowl, combine the raspberry jam, adobo sauce, jalapeno, apple cider vinegar and lemon juice. Pour the jam mixture over the chicken. Cover the slow cooker and cook on low 3-5 hours, until the chicken is tender and cooked through, but not dry.
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Turn off the slow cooker, transfer the chicken to a plate, and use two forks to shred it.
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Pour the sauce left at the bottom of the slow cooker into a medium saucepan. You can strain it if desired.
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Put the shredded chicken back into the slow cooker. Add salt and pepper to taste and then cover the slow cooker to keep the chicken warm.
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Taste the raspberry chipoltle sauce and see if you want to adjust the flavors. For more sweetness, add some honey. For more spice and a more smoky flavor, add more adobo sauce. For even more spice, add some minced jalapeno.
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In a small bowl, mix the cornstarch and water until smooth. Meanwhile, place the pan of sauce on the stove over medium-high heat and bring to a boil. Slowly pour in the cornstarch slurry while whisking the sauce constantly.
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Reduce the heat to a simmer and cook for 1-2 minutes, stirring constantly, until sauce is thick and glossy.
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Pour the desired amount of sauce over the chicken in the slow cooker and stir to combine.
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Serve atop slider buns topped with the slices of cheese and with additional sauce drizzled over the top or used as a dipping sauce.