Butter is graded by the amount of milk solids it contains. Unless you buy exorbitantly priced butter, you've found that using it to sauté something burns the butter. It's not the butter that burns, since butter has quite a high smoking point. It's the milk solids that burn. The economical solution is to clarify your own butter.
You can buy relatively cheap butter at warehouse stores, such as Sam's Club. Clarify butter two pounds at a time. You'll see why that incredibly expensive butter is so expensive after you clarify butter the first time and see how much of it is milk solids. Here's how to do it.
In a large sauté pan over very low heat, place two pounds butter and let it melt. Turn off the heat and let the butter sit at least 20 minutes. This allows a crust to form on the top, and you have to get rid of the crust as well as the milk that has settled to the bottom of the pan.
Cut a double-thick piece of cheesecloth big enough to completely cover the inside of a strainer. Run the cheesecloth under cold water, squeeze out all of the water, then straighten it out and line the strainer with it.
You're going to pick up the pan of butter. It's crucial that you hold it as still as possible, and disturb the milk solids as little as you can.
Pick up the pan, and tilt it to one side. With a slotted spoon, skim the crust from the top and discard. Now, very slowly and carefully pour the butter through the cheesecloth. When you cannot pour any more butter without the milk solids, you're done. Refrigerate the clarified butter.
Note that you have a lot less butter than you began with. That's how much milk is in the butter, and that milk is what burns.
You can use clarified butter at very high temperatures without it burning.