Sauté the aromatics:
In a large saucepan over medium heat, melt the butter. Add the diced onion and cook for about 4 minutes, stirring occasionally, until softened and translucent. Add the minced garlic and cook for another minute until fragrant.
Simmer the base:
Add the chopped potatoes, broccoli stems (set florets aside), and chicken broth to the pan. Bring the mixture to a boil, then reduce to a simmer. Cover and cook for 15 minutes, or until the potatoes and stems are tender when pierced with a fork.
Add the greens:
Stir in the broccoli florets and frozen peas. Simmer uncovered for another 5 minutes, or until the broccoli florets are tender and bright green.
Blend until smooth:
Remove the pan from the heat and use an immersion blender to carefully blend the soup until completely smooth. If you don’t have an immersion blender, transfer the soup in batches to a countertop blender, just be careful with the hot liquid.
Add cream and season:
Stir in the heavy cream until fully incorporated, then season to taste with salt and pepper. Add a little extra broth or water if you prefer a thinner consistency.
Serve and garnish:
Ladle into bowls, sprinkle with fresh chives, and serve warm. Pair with crusty bread or a side salad for a complete meal.