Wipe the portobello caps clean with a damp paper towel and remove the stems. Scrape out the dark gills with a spoon if you want less liquid pooling in the pan.
In a small bowl, whisk the balsamic vinegar, brown sugar, soy sauce and half the minced garlic. Set aside.
Heat 2 tbsp olive oil in a 12-inch skillet over medium-high heat. Season the mushroom caps with salt and pepper on both sides.
Working in two batches of two caps, sear gill-side down for 4 to 5 minutes until deep brown. Flip and sear the other side for 4 minutes. Transfer to a plate and repeat with the remaining oil and caps.
Lower the heat to medium and add the remaining garlic to the same skillet. Cook for 30 seconds until fragrant.
Pour in the balsamic mixture and bring to a simmer. Cook for 3 to 4 minutes, stirring occasionally, until it coats the back of a spoon.
Return all the mushroom caps to the skillet, spooning glaze over each one. Add the butter and thyme, turning the caps to coat, and cook for 2 more minutes until glossy.
Plate the mushroom steaks, spoon any remaining glaze over the top, and scatter with chopped parsley before serving.