Peel and dice the potatoes into even, bite-sized pieces. Chop the onion and mince the garlic. Uniform cuts help everything cook evenly and blend more smoothly.

Heat the olive oil in a large pot over medium heat. Add the chopped onion and cook until soft and translucent, about 5 minutes. Add the minced garlic and cook for one more minute until fragrant.

Add the diced potatoes and vegetable broth to the pot. Bring to a boil over medium-high heat, then reduce to a steady simmer. Cook uncovered until the potatoes are completely fork-tender, about 15 minutes.

Remove the pot from heat and let it rest 2 minutes. Use an immersion blender to blend until smooth, or leave some chunks for a heartier texture. If using a countertop blender, blend in small batches with the lid slightly vented.

Return the pot to low heat. Pour in the heavy cream slowly while stirring. Season with salt and pepper. Warm through for 2 to 3 minutes without boiling. Serve hot, garnished with fresh chives or parsley.