Pour your maple syrup into a heavy-bottomed pot with high walls. Add the cream, butter, or oil.
Prepare a heatproof bowl and fill it about one-third full of ice and a little water. Be sure the bowl is large enough to fit the ice water and the pot together.
Heat the pot over medium, checking the temperature frequently with a candy or instant-read thermometer, until the syrup reaches 235 degrees F. Do not stir.
When the mixture reaches 235 degrees F, immediately turn off the heat and place the pot into the ice bath. Monitor the temperature carefully. Remove the pot from the ice when the mixture is around 100 degrees F.
Stir the thick mixture constantly until the contents of the pot are the color and texture of tahini (this means that fine crystals have formed). You don't need to stir particularly fast, just keep the mixture moving constantly. This may take up to 30 minutes.
Once the tahini color and texture has been reached, immediately funnel the mixture into clean jars. (I got about 12 ounces of maple cream from a little over a pint of syrup.) Seal, label, and store in the refrigerator.