If using fresh peas, shuck the peas.
Put the potatoes in a large saucepan with well-salted cold water to cover them by 3 inches. Cover and bring to a boil over high heat. Cook until tender, about 10 minutes. While the potatoes are cooking, add the peas to the pot. They will float on the top. Cook for 2 or 3 minutes, then remove with a sieve. Cool on a sheet tray.
The potatoes are done when you can easily insert a knife through the potato. When the potatoes are done drain well, scatter on a baking sheet, and let cool for several minutes. Place in the oven to dry out, about 5 minutes. Press the potatoes through a ricer or food mill or mash with a potato masher.
Heat 1 tablespoon of the butter in a large saucepan over medium heat until the butter stops foaming and turns a light brown. Add the garlic and cook quickly until pale gold. Add the 1 1/2 cups of the cream, season, to taste, with salt and pepper and bring to a boil. Reduce the heat to low and beat in the potatoes with a wooden spoon or large whisk. Add the remaining butter by tablespoonfuls, stirring vigorously after each addition. (In this way, the butter does not melt into a golden puddle. Instead, it forms an emulsion with the potatoes, creating a very smooth puree.)
In a small pot, heat the remaining cream until it reaches a boil then simmer for a few minutes. Add the cream to a blender with the peas and puree until smooth. Season with salt and pepper.
Fold the pea puree into the mashed potatoes and adjust seasoning as necessary. Instead of salt, the puree can be seasoned with a little grated Parmesan. Serve hot.
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