In a Dutch oven or large pot, brown the meat over medium-high heat, breaking it up as it cooks. You want no pink left and an internal temperature of 160F. Do not drain the fat; it carries flavor into the next step, and draining it now means you'll be adding oil back in later to make up for it.
Add the chopped onion and garlic to the meat and sauté in the drippings until the onion turns soft and translucent, about 3 to 4 minutes. You'll smell the garlic turn fragrant; that's your cue to move on.
Add the tomato paste and dried herbs to the meat and onion mixture. Stir until the paste darkens slightly and coats the meat; that's the paste's raw edge cooking off.
Pour in the pasta sauce and the chicken stock. Stir to combine; the mixture will look thin at this point, that's expected before it reduces.
Bring the soup to a boil, then reduce to a simmer and let it go for 10 minutes to reduce the liquid slightly. You'll see it start to deepen in color as it thickens.
Add the broken, uncooked lasagna noodles to the soup and stir to combine. Simmer for 10 minutes, or until the noodles are just tender; pull the pot off the heat right at that point, since they'll keep softening in the residual heat.
Just before serving, off the heat, stir in the heavy cream and three-quarters of the shredded mozzarella. The broth will turn from red to a soft, rosy pink; that color change is how you know it's ready.
Serve in bowls, garnished with the remaining shredded cheese. Serve it hot, right off the stove; the soup will continue to thicken as it cools.