Ilsa Heat Diffuser, Made in Italy from Cast Iron, Flame Guard for Simmering, 7-inches

The suggestion of a straight-wall sauté pan is a good one too. Helps with saucier dishes. For your gas stove, have you discovered these heat diffusers? My mom used them when I was growing up and they can make a huge difference in cooking on gas! No more hot spot where the flame ring is, and helps heat the bottom of the pan more evenly, as well as making simmering easier. Cheap ones are available but the design of that Italian made one is really head & shoulders above them. (I do also see these which seem to be very similar & are on a Prime deal rn, looks like mixed info on where they’re made but the design is more similar than the super cheap ones)