Melt half of the butter in a large skillet over medium-high heat. Add half of the mushrooms and thyme and cook, turning once, until the mushrooms are browned, 5 to 7 minutes. Season the mushrooms with salt and transfer them to a paper towel-lined plate. Repeat with the remaining butter, mushrooms, and thyme. Season with salt and transfer them to the plate with the rest of the mushrooms.

Lower the heat to medium and add the garlic to the skillet. Cook until fragrant, stirring constantly, about 10 seconds. Add the cream, white pepper,if using, and the reserved mushrooms. Cook, stirring frequently, until the cream has thickened, 3 to 4 minutes. Season to taste and spoon over the warm blintzes. Garnish with additional thyme and chives if desired.