Get your canning stuff ready. You want to boil the jars and keep them hot for when you pour the jam in later. The lids shouldn't be boiled, but heated; read the instructions for your jars if necessary. The boiling is important to sterilize it all, and the heat later helps create the vacuum seal.
In your dutch oven, put the berries, lemon, and sugar, and bring it all to a boil, stirring frequently so it doesn't burn on the bottom.
Keep the jam heating and reducing. Your goal is to heat it to around 220℉, and keep it going until it reaches a consistency you like.
To test jam consistency, stick a plate in the freezer. Drop a spoonful of jam on the plate and keep it in the freezer for 2-3 minutes, to chill it down to what it would be while refrigerated; that's the consistency the jam will have.
When the jam is more or less ready, add the basil and mix it in, and cook for about another 5 minutes or so. You can taste it to see if you want more basil or not.
When done, spoon or ladle the jam into the hot jars, clean the threads and add the lids, and boil them for another 10 minutes for final sterilization. Remove them from the water and let them sit for a day to ensure they seal.