Preheat your oven to 400°F (200°C). Place two medium enamel baking pans (or one large 9x13-inch baking dish) on the counter. Lightly grease them with a thin film of olive oil or butter to prevent sticking.
Prep the ingredients: Slice the smoked sausage into 1/2-inch coins. Peel the potatoes if you like (the skins can stay on if they’re thin and clean), then cut into 1/2-inch slices or small chunks so they cook evenly. Thinly slice the onion from root to tip into half-moons.
In a large mixing bowl, combine the sliced potatoes and onions. Drizzle with the olive oil and melted butter, then add the kosher salt, black pepper, smoked paprika, dried thyme or Italian seasoning, and garlic (minced or powdered). Toss well with clean hands or a large spoon until everything is evenly coated and the spices are distributed.
Add the smoked sausage coins to the bowl and gently toss again just until the sausage is coated with some of the seasoned oil and mingled with the potatoes and onions. This helps the flavors blend and ensures the sausage browns nicely.
Divide the mixture evenly between the two enamel baking pans, spreading it into an even layer so the sausage and potatoes have room to brown. If using one large dish, spread everything in a single, fairly even layer—crowding too much will steam instead of caramelize.
In a small measuring cup, stir together the chicken broth and the heavy cream or milk (if using). Pour this mixture evenly over the sausage and potatoes in the pans. You don’t want the ingredients swimming; it should just be enough liquid to create steam and a little saucy bottom while the top edges crisp and caramelize.
Cover each pan tightly with foil and place them on the middle oven rack. Bake for 25 to 30 minutes, until the potatoes are starting to turn tender when pierced with the tip of a knife. This covered phase lets everything steam and soften without drying out.
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