Use a heavy-gauge pot, then. It sounds like the recipe called for a dutch oven to promote even simmering. In this case, you can even use a cheap single ply pot. You’ll just need to stand over it and stir continuously to prevent scorching, splatters and to get the right consistency you’re looking for.
Concur. It also sounds (not knowing the recipe) like it wants sufficient surface area for either browning and/or reducing a sauce. A high pot with small surface area might mean you have to work in batches and it will take longer to reduce, while a 12" fry pan might work if there isn’t too much liquid. In both cases, you need to be wary of scorching whatever you are cooking.