Cook the sausage and diced onion over medium-high heat, breaking the sausage into small crumbles, for 8 to 10 minutes until the meat is cooked through and the onion has softened; remove casings first if using links. The sausage should be well browned in spots, and you should see flavorful browned bits on the bottom of the pot.
Drain off the grease, then add the minced garlic and cook for 1 minute. The garlic should smell fragrant right away, and you should hear a quick sizzle as it hits the hot sausage fat left behind.
Sprinkle in the flour and stir well for 1 to 2 minutes. The mixture will look a little pasty at first, then smell lightly nutty instead of raw as the flour cooks out.
Stir in the basil, oregano, cayenne, hot sauce, mustard powder, pepper, and red pepper flakes until the seasonings are evenly distributed. The pot should smell deeply savory and a little sharp from the spices blooming in the heat.
Pour in the chicken broth and scrape the bottom of the pot as you stir, then slowly add the heavy cream. The broth will loosen the browned bits, and the color will shift from dark and meaty to a pale creamy orange.
Bring the soup to a boil, then lower the heat and keep it at a gentle simmer. You want small steady bubbles, not a hard boil, so the cream stays smooth.
Add the kale and tortellini and simmer for 3 to 5 minutes, or follow the package timing if your tortellini needs longer and add the kale during the last 5 minutes. The tortellini should be tender but still hold its shape, and the kale should soften without losing all texture.
Taste the soup and add salt if desired, starting with ¼ tsp and adjusting from there. The broth should taste balanced and lively, not dull or overly salty.
Ladle into bowls and serve right away. The soup should look creamy and full, with sausage crumbles, green kale, and plump tortellini in every scoop.