In a medium pot, heat olive oil over medium heat until shimmering. Add onion, season with salt and pepper, and cook, stirring frequently, until onion is softened, 6 to 8 minutes.

Add potato and roasted garlic, season lightly with salt and pepper and continue to cook, stirring frequently, until onion just begins to brown, about 5 minutes.

Add Parmesan stock, and bring to boil over medium-high heat. Reduce heat to simmer and cook, stirring occasionally, until potatoes are tender and offer little to no resistance when poked with a paring knife, 12 to 15 minutes. Remove from heat.

Using an immersion or countertop blender, blend soup until completely smooth (if using a countertop blender, blend in batches, if necessary, and start blending at low speed before increasing to high). If soup is too thick, thin as needed with additional Parmesan stock. Season to taste with salt and pepper, and a pinch of nutmeg.

Divide soup between warmed bowls, sprinkle with basil and red pepper flakes, and serve, passing bread at the table.