In a saucepan, heat the heavy cream over low to medium heat until it reaches a temperature of 180°F (82°C). Use a thermometer to monitor the temperature and avoid boiling the cream.
Remove the saucepan from the heat and add the lemon juice or white vinegar. Stir gently to incorporate the acid into the cream.
Let the mixture sit undisturbed at room temperature for about 30 minutes to an hour. During this time, the acid will cause the cream to curdle and thicken.
Line a fine-mesh sieve or colander with cheesecloth and place it over a bowl or in the sink.
Carefully pour the curdled cream into the cheesecloth-lined sieve, allowing the whey (liquid) to drain away. The longer you let it drain, the thicker the resulting mascarpone will be.
Once most of the whey has drained, gather the edges of the cheesecloth and gently twist it to remove any remaining liquid.
Transfer the mascarpone cheese to an airtight container and refrigerate for at least 4 hours or overnight to allow it to set further and develop its flavor.
Your homemade mascarpone cheese is now ready to be enjoyed!