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Preheat the oven to 325 F. Line baking sheets with parchment paper or silicone mats. Have all ingredients measured and ready before beginning.
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Melt the butter in a large saucepan. After it is melted, whisk the butter constantly over medium heat until it is nicely browned but not burnt.
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Turn off the heat and dump in the sugar, honey and fine sea salt. Mix until smooth with no lumps of brown sugar. Mix in the oats and baking powder. Let stand to cool for a few minutes.
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Stir the flour into the dough until evenly incorporated. Let the dough stand for 5 minutes to firm up. Using a small cookie scoop (about 1 1/2 inches diameter), scoop mounds of cookie dough onto a baking sheet at least 2 inches apart. Sprinkle with the coarse sea salt, to taste.
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Bake for 10-13 minutes, until brown at the edges and darker in the middle. Watch carefully toward the end, when the browning becomes more rapid. Let cookies cool on the baking sheet for 3-5 minutes and then carefully transfer to a cooling rack.