Caramelized Onions:
In a large cast-iron skillet over medium heat, melt the butter. Add the sliced onions and sauté for about 5 minutes until they start to soften and shrink.
Lower the heat to low, sprinkle in the sugar, dried thyme, and stir. Continue cooking for 20-30 minutes, stirring every 5 minutes, until the onions are golden and caramelized. If the onions are caramelizing too quickly, reduce the heat further.
Once caramelized, add the balsamic vinegar to deglaze the pan and season with ¼ teaspoon salt. Stir well, allowing the onions to absorb the vinegar. Remove from heat and let cool to room temperature. You can refrigerate the onions for later use or proceed with making the biscuits.
Biscuit Batter:
Preheat the oven to 450°F (230°C) and position a rack in the center. Line a baking sheet with parchment paper or a silicone mat and set aside.
Melt 1 stick of butter (about 10 tablespoons) in a microwave-safe bowl (around 45 seconds) and set aside.
In a large mixing bowl, whisk together the flour, sugar, baking powder, garlic powder, dried parsley, and kosher salt.
Add the melted butter and ¾ cup of milk to the dry ingredients. Use a rubber spatula to fold the ingredients together until combined.
Gently fold in the caramelized onions and shredded Gruyere cheese. If the dough seems dry, add additional milk 1 tablespoon at a time (up to 4 tablespoons) until the dough comes together. The dough should not be too wet.
Bake:
Drop 2-tablespoon portions of dough onto the prepared baking sheet, spacing them evenly apart.
Bake the biscuits for 10-12 minutes or until golden brown on the outside.
Meanwhile, melt the remaining 2 tablespoons of butter in a microwave (about 20 seconds). Stir in a pinch of dried parsley if desired.
Brush the freshly baked biscuits with the melted butter mixture and serve warm.