Preheat your oven to 350 degrees F (175 degrees C).
Coat Tomato (2.25 pound) and Yellow Onion (1/4) with Olive Oil (2 tablespoon) and season with Kosher Salt (1 teaspoon) and Ground Black Pepper (to taste) and roast on a cookie sheet for 45 minutes or until the skins of the tomatoes are peeling away. Remove from the oven and let cool so you can take the skins off.
Once cool enough to handle, peel off the skins and transfer tomatoes and onions, and all the juices into a large pot.
Add the Apple Cider Vinegar (1/4 cup) and Brown Sugar (1 tablespoon) into the large pot. Simmer on medium-low heat until reduced about halfway.
After it has reduced, add the Fresh Thyme Leaves (1 teaspoon) and let stand while you make the cheesy shortbread cookies.
In a mixing bowl fitted with a paddle attachment, whip the Butter (4 ounce) until fluffy.
Once whipped, add the White Cheddar Cheese (2 ounce), All-Purpose Flour (1 1/4 cup), Fresh Rosemary (1/8 teaspoon), Fresh Thyme Leaves (1/4 teaspoon), Kosher Salt (1/4 teaspoon), and Ground Black Pepper (to taste) until it forms a cohesive dough. Form a disk, wrap and chill for 30 minutes.
Remove the dough from the refrigerator and form balls (about 1 ½ to 2 inches) and either using your thumb or the back of a small measuring spoon make an indentation for the tomato jam.
Dollop the jam onto the cookies and bake at 350 degrees F (175 degrees C) for 20-25 minutes or until golden brown.