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Preheat grill to 350ºF
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Wash peaches and pat dry. Cut them vertically and twist the halves to separate from the pit. If the pit is still hanging on dig it out with a grapefruit spoon.
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Grease grill grates with a paper towel soaked in oil. Place peach halves face down on the grill and sprinkle with brown sugar. Close lid and cook for 5 minutes.
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Using tongs, flip peaches and equally divide remaining sugar amongst the peach halves. Close lid and cook for an additional 5 minutes. Transfer peaches to a baking pan and let cool for a couple of minutes.
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Toss peaches in a blender and pulse until coarsely pureed.
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(Optional Step) Sterlize Jars and lids. Put 2 quart or 6 half pint jars on a wire rack in a large pot. Fill the pot with water until it covers the jars. Bring to a boil. Boil for 10 minutes and turn off the heat. Meanwhile do the same thing in a smaller pot with the lids and rings and a stainless steel canning funnel. When the 10 minutes are up, turn off the heat and let them sit in the water until ready for use.
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Pour the peaches into a large, heavy bottomed pot and add the sugar, lemon juice, bourbon, cinnamon, vanilla bean, and butter.
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Turn the burner on to medium-high heat and stir the mixture. Let it come to a rolling boil.
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Add the pectin and let it come to a boil again. Reduce heat to medium and cook until reduced by 1/4 (about 20 minutes).
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Remove the pot from heat, discard the cinnamon sticks and vanilla bean.
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Ladle the jam into the jars and don’t forget to use the canning funnel. Cover the jars with the lids and screw on the bands. They should be almost tight.
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Put the jars back in pot you boiled them in, lid side up. Cover the pot and bring it to a boil again. Boil for 10 minutes.
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Remove lid and let the jars rest for 5 minutes in the water. Take the jars of jam out and let them chill and set on the counter overnight.