Cup of Yum
1. In a medium skillet, melt the butter over medium heat. The butter will foam up and might spatter a bit. Continue cooking, stirring often, until the butter turns golden brown and the milk solids turn from yellow to chestnut red to brown, 5-10 minutes. Immediately transfer to a heat-proof bowl and let cool.
2. Grease a large bowl with the vegetable oil.
3. In a large bowl or the bowl of a stand mixer fitted with a dough hook, mix the flour, sugar, yeast, and salt. In a small saucepan, heat the milk until a thermometer registers 120°F - 125°F. Add the milk to the dry ingredients and stir until mixed. Add the egg and stir to mix well. Knead until a smooth dough forms, 5 to 10 minutes.
4. Gradually mix in ½ cup of the cooled browned butter. The dough will separate a bit, but keep on mixing and it will come together. Knead until the dough is soft and completely combined, this could take 5 minutes. Transfer the dough to the greased bowl and turn to coat. Cover with a tea towel and set in a warm place until doubled in volume, about 1 hour.
5. Meanwhile, butter a 9x13-inch baking pan.
6. Transfer the dough to a work surface. Press into an 8x10-inch rectangle. Using a sharp knife, cut the rectangle into 12 equal pieces.
7. Working with 1 piece at a time, press into about a 3 ½-inch square or round. Pinch the edges firmly together, then turn over and roll into a ball. Place in the prepared baking dish.
8. Cover the rolls with a tea towel and set in a warm area until doubled in size, 40 minutes to 1 hour.
9. Preheat the oven to 400°F. In a small bowl, make the egg wash by whisking the egg and milk together. Brush the egg wash generously over the tops and sides of the rolls.
10. Bake the rolls until deep golden brown, about 18 minutes. Transfer the pan to a rack. Melt the remaining browned butter and brush generously over the rolls; sprinkle with flaky salt. Let cool in the pan for 30 minutes. Serve with butter.

Variation: Brown Butter Dinner Rolls Stuffed with Feta and Zataar

Cup of Yum
1. In a medium skillet, melt the butter over medium heat. The butter will foam up and might spatter a bit. Continue cooking, stirring often, until the butter turns golden brown and the milk solids turn from yellow to chestnut red to brown, 5-10 minutes. Immediately transfer to a heat-proof bowl and let cool.
2. Grease a large bowl with the vegetable oil.
3. In a large bowl or the bowl of a stand mixer fitted with a dough hook, mix the flour, sugar, yeast, and salt. In a small saucepan, heat the milk until a thermometer registers 120°F - 125°F. Add the milk to the dry ingredients and stir until mixed. Add the egg and stir to mix well. Knead until a smooth dough forms, 5 to 10 minutes.
4. Gradually mix in ½ cup of the cooled browned butter. The dough will separate a bit, but keep on mixing and it will come together. Knead until the dough is soft and completely combined, could take about 5 minutes. Transfer the dough to the greased bowl and turn to coat. Cover with a tea towel and set in a warm place until doubled in volume, about 1 hour.
5. Meanwhile, butter a 9x13-inch baking pan. In a small bowl, mix the feta cheese, sesame seeds, zataar, and sumac.
6. Transfer the dough to a work surface. Press into an 8x10-inch rectangle. Using a sharp knife, cut the rectangle into 12 equal pieces.
7. Working with 1 piece at a time, press into about a 3 ½-inch square or round. Sprinkle with 1 rounded teaspoonful of the feta cheese blend. Gather the edges together to encase the spice blend. Pinch the edges firmly together, then turn over and roll into a ball. Place in the prepared baking dish.
8. Cover the rolls with a tea towel and set in a warm area until doubled in volume, 40 minutes to 1 hour.
9. Preheat the oven to 400°F. In a small bowl, make the egg wash by whisking 1 large egg and 2 tbsp milk together. Brush the egg wash generously over the tops and sides of the rolls. Sprinkle the remaining spice mixture over the top of the rolls. 
10. Bake the rolls until deep golden brown, about 18 minutes. Transfer the pan to a rack. Melt the remaining browned butter and brush generously over the rolls; sprinkle with flaky salt. Let cool in the pan for 30 minutes. Serve with butter.