To make the compote, combine the blueberries, Swerve, water, and lemon juice in a heavy-bottomed saucepan. Heat on medium heat, stirring occasionally, until the blueberries begin to pop and the liquid boils. Add the basil, stirring occasionally, until most of the blueberries have reduced and the liquid begins to thicken. Simmer without stirring for another five minutes, then stir again, remove from heat, and let cool to room temperature.
Prepare your sous vide water bath, making sure that the water will not cover the jar lids. Set it for 175 degrees Fahrenheit (80 Celsius).
In a large mixing bowl, use a hand mixer to blend the cream cheese, Swerve, and salt. Add the eggs and lemon juice and blend some more, then finally add the sour cream and heavy cream and blend until it's completely smooth, scraping down the sides as necessary.
Fill each jar with the cheesecake batter to the bottom of the lid line. Seal the jars loosely using your fingertips instead of your whole hand, and carefully place in the water bath. Leave them undisturbed in the water bath for 90 minutes, then remove with tongs and leave on the counter to cool.
Once the jars have cooled to a temperature where you can handle them, remove the lids and add enough compote to cover the top of each, about 2 teaspoons. If desired, sprinkle with toasted nuts. Place the lids back on and put in the refrigerator to cool. Serve fully chilled.
Macros for each serving, counting using half of the coulis: 239 calories, 7 grams net carbs, 7 grams protein, 20 grams fat.