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1
Place a small plate in the freezer so you can test the jam for proper thickness later.
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2
Use a zester to remove the zest from half of the oranges and two of the lemons. Add the zest to a large, deep, heavy-bottomed pot. Remove the remaining peels from all of fruit. Wrap the peels in a cheesecloth bag, tied up with a string so it doesn't fall open, and add the bag to the pot.
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3
Use a sharp knife to cut the oranges and lemons in between the pith into clean segements making sure to work over a bowl to catch any escaping juice. Squeeze remaining pith and discard. Pulse the fruit in a food processor two or three times, just enough to chop the segments into coarse chunks that are about 1/2-inch across. Add the fruit to the pot with the zest and peels. Strain the juice you saved while segmenting the fruit and add it to the pot, along with the rest of the orange and lemon juice.
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4
Add 2 1/2 cups of water to the pot and bring to a boil over medium heat. Once boiling, lower heat to low and simmer for 25 minutes. Remove from heat and allow to cool. Once the bag of rinds is cool enough to touch, use your hands to wring as much juice as possible from the rinds. Discard the bag.
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5
Add ginger, vanilla, sugar, and butter to the pot, stirring well to combine. Cook over medium heat, stirring frequently, until the fruit begins to bubble and spit. Cook for 15 minutes longer, stirring frequently to keep the fruit from sticking to the bottom of the pot, and lower heat if threatening to stick. Add sesame seeds and cook for another 15 minutes, continually stirring to keep the bottom from burning.
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6
Begin testing the marmalade for doneness: Spread 1/2 teaspoon of cooked fruit on the cold plate and place it back in the freezer. Wait 30 seconds, then run your finger through the fruit. It should be thick enough to maintain a path when you run your finger through it. If you'd like thicker marmalade, place the plate back in the freezer and cook the fruit for another 4 minutes and test again. Repeat until desired thickness is achieved, but be careful about cooking too long or you will alter the taste of your marmalade.
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7
Remove pot from heat and use a spoon to skim any foam from the surface of the fruit. Ladle marmalade into sterilized jars and process them in a hot water bath for 10 minutes. Unopened jars will keep at room temperature for up to 6 months. Opened marmalade should be refrigerated.
