Mix the ground turkey, ricotta, mustard, shallot, basil, salt, and pepper together in a large bowl. Form into 12 small 1/2-inch thick patties.
Brush the grill grates with olive oil with a clean tea towel to keep the turkey from sticking. Grill the patties for 4 minutes, and then flip and continue to cook the other side for another 3 minutes. Place the rolls on the warmer rack to toast during the last 3 minutes of grilling.
To assemble burgers, place a patty between the buns and top with lettuce and Tomato Jam.
Add all the ingredients to a medium saucepan and bring to a boil over high heat. Reduce the heat and simmer, stirring occasionally, until the tomatoes have dissolved and what remains is a thick jam-like consistency, about 1 hour. Cool before serving. The jam can be stored in an airtight mason jar for up to 2 weeks in your refrigerator.
Adding the ricotta cheese to the turkey burger mixture helps to keep it moist and flavorful without adding a lot of fat. This is a great recipe to double up on when tomatoes are at their ripest and best during the summer months.