Heat olive oil in a large pot over high heat. Once hot, add the sausage and sear for about a minute per side. Crumble and cook until deeply browned. Remove with a slotted spoon to a paper towel-lined plate, leaving 2–3 tablespoons of grease in the pot. Drain off excess if there is more than that.
Add onion, celery, and carrot to the pot. Cook, stirring occasionally, for 7–9 minutes, or until tender. Add garlic and cook for 30 seconds, stirring constantly.
Stir in salt, pepper, Italian seasoning, parsley, oregano, and thyme. Mix for about 15 seconds, then add butter and stir until melted.
Sprinkle flour over vegetables and whisk constantly for 1 minute. Slowly pour in the broth, whisking until smooth and slightly thickened. Gradually whisk in the milk and cream, then bring to a gentle boil.
Once boiling, reduce the heat to medium. Add the gnocchi, kale, and cooked sausage. Simmer for 2–4 minutes, or until the gnocchi is tender. Taste and adjust seasoning as needed.
Ladle into bowls and top with fresh thyme if desired. Serve with hearty buttered bread on the side.
