Prepare a medium gas or charcoal grill fire.
Meanwhile, in a small saucepan, combine the tomatoes, vinegar, sugar, thyme, 1/4 tsp. salt, and 1/8 tsp. pepper. Bring to a boil over medium-high heat, reduce the heat to medium, and simmer, stirring often, until most of the liquid has evaporated and the mixture resembles a thick, chunky ketchup, about 20 minutes. Season to taste with salt and pepper; set aside.
Grill the sausages, turning occasionally, until cooked through and dark golden-brown all over, 10 to 15 minutes. During the last few minutes of cooking, toast the sandwich rolls on the grill, 30 seconds to 1 minute per side.
While the sausages are cooking, heat the oil and the cumin seed in a small saucepan over medium heat until fragrant, 2 to 3 minutes. Add the sauerkraut, broth, 1/4 tsp. salt, and 1/8 tsp. pepper and bring to a boil. Cover, reduce the heat to medium low and simmer, stirring occasionally, for 10 minutes. Season to taste with salt and pepper.
Spread the rolls with some of the tomato jam and then place a sausage inside each. Top the sausages with the sauerkraut and serve.