Preheat oven to 275 degrees F, and prepare a baking sheet with parchment paper.
Place the sourdough slices on the prepared baking sheet, and toast in the oven for 10 minutes, or until lightly browned. Transfer to a cutting board.
Cut the toasted sourdough slices into 1 inch cubes. Turn oven temperature up to 350 degrees F.
In a large frying pan (light colored pan is best), melt the butter over medium heat, then add the sage leaves. The butter will start to foam, and after the foam dissipates you should start to see lightly browned specks forming at the bottom of the pan. Stir continuously to avoid burning. Keep an eye on the sage, and remove with a slotted spoon if it starts to get too crispy before the butter is ready. Place on a paper towel-lined plate.
After about 5-8 minutes, the butter should have turned golden brown, with a very nutty aroma. Turn off the heat, remove the sage leaves if you haven't already, then immediately add in the sourdough cubes and toss quickly to combine (the bread will soak up that butter fast, so you want to mix quickly and thoroughly to evenly disperse brown butter).
Return sourdough cubes to baking sheet, sprinkle with flakey sea salt, and bake for 6-8 minutes, tossing halfway through, until golden brown. Set aside.