Step 1

Set a 6-quart Instant Pot® to high saute (see Cook's Note). Add the butter and olive oil to the pot. Once the butter has melted completely, add the onions, thyme, sugar, 1/2 teaspoon of salt and several grinds of pepper. Cook, stirring, until the onions start to sizzle and the mixture is thoroughly combined, 1 to 2 minutes.

Step 2

Follow the manufacturer's guide for locking the lid and preparing to cook. Set to pressure cook on high for 4 minutes. After the pressure-cook cycle is complete, follow the manufacturer's guide for quick release and wait until the quick-release cycle is complete (this should take about 2 minutes). Being careful of any remaining steam, unlock and remove the lid, then stir in the balsamic vinegar. At this point, the onions should be tender and blonde in color.

Step 3

Set the pot back to high saute and cook, stirring frequently and scraping any brown bits from the bottom and sides of the pot, until almost all the liquid has evaporated and the onions are a deep golden brown and saucy, about 30 minutes. Be sure to stir the onions frequently and watch them closely; you want to scrape the brown bits from the pot before they turn too dark and burn. Remove the thyme stems; taste and adjust the seasoning with salt and pepper.