Pat the fish dry with a paper towel on both sides. Season the fish with salt and pepper, then set aside.
Heat a large stainless steel skillet over medium high heat. After a few minutes, splash a little bit of water onto the pan. If the water steams and bubbles, your pan is not hot enough. If the water dances on top of the pan in a bubble that won’t burst, your pan is hot enough to move forward!
Season the skillet with enough oil to comfortably coat the surface (about 1 tbsp or so.) It should thin out and shimmer right away, and may be slightly smoky.
Place the dried off fish into the skillet and let it cook for about 2 minutes, until slightly golden on the bottom facing the heat. If you don't have enough space for all of your fish, work in batches. They only take a few minutes to sear. Gently flip each fillet and cook until the fish measures at least 140 degrees F internally. If you don’t have a meat thermometer, you’ll know the cod is done when it becomes delicate and may even flake when it’s touched. If it flakes, it will still taste fabulous and you can still plate it nicely, so don’t worry!
Turn the stove off. Then, remove the cod from the skillet and place the fillets onto a plate (be careful, they will be fragile!). Cover the plate with tin foil so they stay warm.
Return back to your skillet and let it cool for 1-2 minutes
Then, adjust the heat to medium low and add the butter to the pan along with a small pinch of salt (about 1/8 tsp.)
The butter should slowly melt, maintaining its foggy light yellow color. Once the butter is fully melted, add the shallots and sage to the pan.
Adjust the heat to medium/medium high. The butter should begin to bubble, and will also be slightly frying the shallots and sage. Watch the butter closely and swirl it around the pan to see if any brown butter deposits start to form. You will know the butter is browning when it begins to smell slightly sweet and caramel-like, and you will also see golden brown deposits on the bottom of the pan. Simultaneously, the shallots and sage should be adequately fried -- the sage should be a dark brown green and stiff to touch, and the shallots should become a darker golden brown with a fried, flaky texture. Once the butter, shallots and sage look and smell as described above, remove the pan from the heat and pour it into a bowl. This will stop it from cooking.
Plate the fish however you would like, then pour the brown butter sauce on top, making sure to also top with shallots and sage. Serve immediately and enjoy!