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Preheat the oven to 400 degrees Fahrenheit. Arrange the diced sesame seed buns in a single layer on a baking sheet lined with parchment paper. Evenly drizzle the pieces with olive oil and place them in the oven for approximately 10 minutes or until they attain a crisp exterior.
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In a large pot set over medium heat, add the ground beef, one teaspoon each of dried oregano and thyme, and season with kosher salt and freshly cracked pepper. Ensure the beef is thoroughly cooked, breaking it apart with a spatula. Once cooked, transfer the beef to a separate container and set aside.
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In the same pot, melt 6 tablespoons of unsalted butter over medium heat.
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Introduce the diced onion, sliced carrots, and sliced celery to the pot. Adjust the heat to medium-high and sauté the vegetables, occasionally stirring, for approximately 10 minutes.
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Reduce the heat to medium and incorporate the minced garlic, the remaining dried oregano, and dried thyme. Allow these to cook for an additional minute.
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Sprinkle the vegetables with the all-purpose flour, ensuring they are evenly coated. Continue to cook for another minute, stirring consistently.
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Deglaze the pot by introducing a small quantity of chicken broth, ensuring to scrape and incorporate the residue at the bottom of the pot.
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Incorporate the remaining chicken broth and the uncooked elbow macaroni. Season with additional kosher salt and freshly cracked pepper, then increase the heat to medium-high until the mixture reaches a simmer.
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Once simmering, decrease the heat to low and allow the mixture to simmer for 5-7 minutes or until the macaroni is al dente, ensuring to stir occasionally to prevent the pasta from adhering to the pot’s base.
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Remove the pot from the heat and stir in the heavy cream followed by the shredded cheddar cheese.
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Add the white balsamic vinegar and return the previously cooked ground beef to the pot. Stir and let it warm over medium heat until thoroughly heated. Taste and adjust seasoning if necessary.
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Serve the soup in individual bowls, garnishing with the previously prepared sesame seed bun croutons, finely sliced green onions, and additional shredded cheddar cheese.
