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Prepare your jam jars by sterilizing them in the dishwasher on the sterilize cycle or simmer the jars and lids in water on the stovetop for 15 minutes. Let them air dry on a rack.
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Place 2 to 3 small plates in the freezer. You will use these later to test the gel point of the jam.
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Heat a large stockpot over low heat. Add the blackberries, lemon juice, and sparkling wine. Stir in the pectin until dissolved. Bring the mixture to a boil that is vigorous enough that it continues to boil even when stirred down.
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Add all the sugar at once. The mixture may bubble up, but it will settle down and the sugar will dissolve. Swirl the pot to dissolve the sugar, but do not stir with a spoon. Turn up the heat and bring everything back to a strong boil. Continue to boil vigorously for 1 minute. Turn off the heat and skim away any foam that rises to the surface.
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Test to see if the jam has set by dropping a teaspoon of jam onto one of the plates from the freezer. If the jam has reached its gel point it will set up quickly on the plate. If the consistency is good, proceed to the next step. If the jam is too thin, continue to boil it, checking every 5 minutes with a new plate from the freezer.
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When the jam is the right consistency, add the cassis. Strain the jam through a fine mesh strainer to remove the blackberry seeds, using a spatula to push as much of the jam through the strainer as possible. Use a wide-mouth funnel to fill the sterilized jars with hot jelly, leaving ½-inch of room at the top. Wipe any jelly from the top and sides of the jars with a clean towel. Screw on the lids, but do not over-tighten.
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Preserve the jam for long storage by using the water bath canning method or simply refrigerate the jars and eat within 2 to 3 weeks.