This is my rendition of the classic, made by a guy (me) who normally doesn't like liver. Do my optional steps if you're like me. If you love liver, you can skip the pre-soaking.
Optional pre-soak. If you want, and I recommend it, to tame the odor of the liver, cut them into pieces between 1/4 and 1/2 inch thick, and as large as you want. Soak these overnight in a brine of 1/4 cup kosher or sea salt to 1 quart water. Soak in the fridge. The next morning, discard the brine and soak in milk or buttermilk up to another 8 hours. Rinse under cold water and pat dry.
Heat the butter in a large pan over medium-high heat. Add the sliced onions. They will mound up and be awkward at first, but keep cooking them and stirring until they wilt. When they do, salt the onions lightly. Stir and cook until you see just a little browning, then drop the heat to medium. Keep cooking, stirring occasionally, until the onions brown more deeply. You might need to drop the heat to low and/or cover the pan to keep things from scorching or sticking.
When the onions are close to being done, add the thyme and honey, if using. Let this cook another 10 to 20 minutes -- up to you. Remove from the heat.
In another pan, add a few tablespoons of high-heat oil, like canola, grapeseed or avocado oil, and get this hot over medium-high heat. As that is heating, dust the liver pieces in the flour. Press the flour into the meat well on both sides. Note: If you did not brine the livers, you do need to salt them before flouring.
Sear the livers in the hot oil for no more than 90 seconds per side. You want the livers to be pink in the center. It's better to slightly undercook than overcook deer liver, since overcooked liver gets dry and chalky.
To finish, serve the livers over a bed of the caramelized onions, with some bread or potatoes. Grind some black pepper and squeeze some lemon juice over them when you serve.
Notes
Keep in mind this recipe works with all large mammal livers.