Heat your skillet over medium-high heat and add the oil once it's hot. Lay the brats in a single layer and brown them for about 1 to 2 minutes per side, just until they're golden all over. Remove them from the pan and set them aside while you work on the onions.
Lower the heat to medium and melt the butter in the same skillet you used for the brats. Add the sliced onions along with the brown sugar, thyme, salt, pepper, and paprika, stirring occasionally until they turn soft and just start to caramelize.
Pour the dark lager right over the softened onions and stir well, scraping up any browned bits stuck to the bottom of the pan. This step is where all that concentrated flavor gets released back into the sauce.
Stir in the beef stock, then nestle the browned bratwurst back into the skillet, making sure they're mostly submerged in the beer sauce. Let everything simmer gently until the sauce thickens and the sausages are cooked through.
Once the brats reach a safe internal temperature, or once the sauce has thickened nicely if using pre-cooked links, pull the skillet off the heat. Let everything rest for a couple of minutes before plating so the flavors settle.