In a large saucepan, add water and lightly salt. Add grits and bay leaf. Bring to a boil over medium-high heat, then remove from heat, cover, and let sit offheat 15 minutes to soak grits.
Return grits to medium-low heat and uncover. Cook grits over medium-low heat, stirring occasionally until water is absorbed and grits are tender, about 15-20 minutes.
Remove grits from heat and discard bay leaf. Fold heavy cream into grits with a rubber spatula until smooth. Season grits with additional salt and pepper to taste, cover, and keep warm while you make the mushrooms.
Melt butter in a large skillet over medium-high heat. Add mushrooms and saute 3-5 minutes until tender. Add garlic and thyme and cook 1 additional minute until fragrant. Season with salt and pepper to taste.
Divide grits between 4 serving bowls and top with sauteed mushrooms, cooked eggs of your choice, and grated asiago cheese. Serve immediately and enjoy!