Heat a large skillet over medium heat and lay the bacon slices in a single layer. Cook until crisp on both sides, then transfer to a plate lined with a paper towel. Leave the rendered fat in the pan instead of wiping it out, since it adds so much flavor to the chicken.
Season the chicken breast generously with salt and pepper, then place it in the same skillet with the leftover bacon fat. Cook for about 5-6 minutes per side until fully cooked through and golden. Let it rest a few minutes before slicing thinly on a diagonal.
While the chicken cooks, heat a teaspoon of ghee or oil in a small skillet over medium-low heat. Add the sliced onion and cook slowly for around 20 minutes, stirring occasionally, until soft, sweet, and lightly caramelized. Don't rush this step or the onions won't develop that deep flavor.
Lay two slices of bread down and layer the sliced chicken evenly across them. Top with the caramelized onion, then a generous layer of brie slices, followed by a sprinkle of fresh thyme leaves. Close each sandwich with the remaining bread slices, pressing down gently.
Brush the outside of the bread lightly with oil, then place the sandwiches on a panini press or in a skillet with a heavy pan on top. Cook for about 2 minutes per side, or until the bread is golden and crisp and the brie has fully melted inside.
Let the panini rest for a minute before slicing in half, since the melted brie needs a moment to settle. Serve immediately while the cheese is still warm and gooey for the best texture.