I usually get all complicated with caramelized onions by doing at least eight onions at time, cooking it all low and slow, and never letting it brown. Just know you don’t have to, and you can caramelize them any way you like. Here's a simple way to do just one onion. Throw a sliced onion, butter, olive oil, salt, and a sprig of thyme into a heavy-bottomed pot (cast iron or Dutch oven works great). Then cook for a few minutes on medium, put on a lid, and turn the heat all the way down. Check on it every 15 minutes or so to make sure it's not sticking. Add some water or chicken stock if necessary. It will take about an hour. If you have some excess liquid at the end, remove the lid and reduce it down for a few minutes.
Line a sheet pan with parchment paper or a Silpat. Cut puff pastry into four 4-inch by 4-inch squares (though honestly, any shape is fine). Save remaining scraps for another use. Place squares on sheet pan.
For each tart: Spoon a tablespoon of caramelized onion into the center of the square, making sure you leave at least a 1-inch border all around. Wrap an anchovy fillet around an olive and press the little bundle down into the onion. Fold all 4 corners of the puff pastry in towards the center.
Place sheet pan in the oven. About 10 minutes in, pour a tiny bit of balsamic on each olive and let it drip down a bit onto the onions. Just for fun. Just because the resulting color is so beautiful. And the flavor so sweet. Keep an eye on the tarts. You want the pastry cooked through and the onions to have a nice deep brown color. Depending on your oven, this takes about 15 minutes. If you're not sure, take one out and look and poke. You will know.
Eat them the day they're made. Or freeze them. They reheat beautifully.
Phyllis Grant is an IACP finalist for Personal Essays/Memoir Writing and a three-time Saveur Food Blog Awards finalist for her blog, Dash and Bella. Her essays and recipes have been published in a dozen anthologies and cookbooks including Best Food Writing 2015 and 2016. Her work has been featured both in print and online for various outlets, including Oprah, The New York Times, Food52, Saveur, The Huffington Post, Time Magazine, The San Francisco Chronicle, Tasting Table and Salon. Her memoir with recipes, Everything Is Out of Control, is coming out April 2020 from Farrar Straus & Giroux. She lives in Berkeley, California with her husband and two children.