Preheat the oven to 375°F (190°C).
Slice the tops off the onions and carefully hollow out the centers, leaving about ¼ inch of onion around the edges. Set the hollowed onions aside.
In a saucepan over medium heat, melt the butter. Add the minced garlic and sauté for about 1 minute until fragrant.
Stir in the flour and cook for an additional minute to form a roux.
Gradually whisk in the heavy cream and milk, stirring constantly until the mixture thickens (about 3-5 minutes).
Remove the saucepan from heat and stir in ¾ cup of the shredded Asiago cheese, salt, pepper, and dried thyme. Mix until the cheese is melted and the sauce is smooth.
Place the hollowed onions in the baking dish. Carefully pour the creamy cheese sauce into each onion until filled.
Top each onion with the remaining Asiago cheese.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15 minutes or until the cheese is golden and bubbly.
Remove from the oven and let cool for a few minutes. Garnish with chopped fresh parsley before serving.