In a small saucepan, stir together the balsamic, berries, wine, honey, Dijon, garlic and sprigs of thyme. Bring to a boil over medium-high heat, stirring occasionally. Reduce to a simmer and allow mixture to cook, stirring occasionally, until it has thickened and reduced by at least half, about 15 minutes. Remove from heat, remove thyme sprigs and set mixture aside; it will continue to thicken off the heat.
Meanwhile, heat the cooking oil or butter in a nonstick skillet over medium-high heat. If using butter, heat it until the foam subsides and it turns a deep golden brown, about 3 minutes.
Season both sides of the salmon with salt and pepper. When skillet is ready, add salmon to the skillet skin-side up. Cook without flipping for 3 to 5 minutes or until the fish turns a nice deep crispy brown. Flip the fish and allow it to cook to desired doneness, about 3 minutes more depending on thickness.
To serve, drizzle a little of the reduction, a teaspoon or two, on each of four individual serving plates. Place the salmon on top of the drizzle then top each fillet with more of the reduction, being sure to include a few of the berries. Finish the presentation with fresh thyme and lemon slices. Serve immediately.