I start by patting the chicken breasts completely dry with a paper towel, since moisture stops a good sear from forming. Then I season both sides generously with salt, pepper, and oregano. Letting the chicken sit at room temperature for a few minutes helps it cook more evenly once it hits the pan.
I heat olive oil in a large skillet over medium-high heat until it shimmers slightly. Once hot, I lay the chicken in carefully and let it sear undisturbed for about 5 to 6 minutes per side. I don't move it around too much, since that's what gives me that gorgeous golden crust.
Using my meat thermometer, I check that the chicken has reached 165°F internally before pulling it out of the pan. I set it aside on a plate and tent it loosely with foil. Resting the chicken keeps all those juices locked in instead of spilling out when I slice it later.
In the same skillet, I melt the butter and toss in the minced garlic, stirring for about 30 seconds until fragrant. I then pour in the white wine, scraping up all those flavorful browned bits stuck to the pan. This step is where most of the dish's depth of flavor actually comes from.
Once the wine reduces slightly, I stir in the chicken broth and let it simmer for a couple of minutes. Then I lower the heat and pour in the heavy cream, whisking gently so everything blends into a smooth, pale sauce. This is the base that will carry the brie.
I cut the brie into small chunks and drop them into the simmering sauce, whisking continuously until every piece melts completely. The sauce turns thick, glossy, and irresistible at this point. I keep the heat low so the cheese doesn't separate or turn grainy.
Finally, I nestle the chicken back into the skillet, spooning that brie sauce generously over the top. I let it warm through for a minute, sprinkle on fresh thyme, and serve it immediately while the sauce is still warm and silky.