Save time by prepping the parsley and green onions while the potatoes are cooking.
1 Boil the potatoes: Place the peeled and cut potatoes and the thyme in a medium (2 quart) saucepan and cover with cold water. Add two teaspoons of salt to the water.
Bring to a boil and reduce heat to maintain a low simmer. Simmer for 15 to 20 minutes until the potatoes are easily pierced with a fork.
2 Purée parsley and green onions with milk: While the potatoes are cooking, chop up the parsley and the green onions. Place the chopped green onions and parsley in a food processor. Add a teaspoon of salt and the 1/4 cup of the milk. Pulse until smooth.
3 Drain potatoes, heat milk, cream, butter: When the potatoes are done, drain them in a colander and place them in a large bowl. Discard the thyme sprigs. Return the still hot, empty pot to the stove and add the remaining milk, cream, and butter. Heat on low heat until the butter is melted.
4 Mash the potatoes: While the milk is heating, mash the cooked potatoes with a potato masher or use a potato ricer. (Do not over mix or the potatoes will turn gluey.)
5 Stir mashed potatoes into heated milk and cream, stir in parsley purée: Return the mashed potatoes to the pot with the milk mixture and stir to combine. Turn off the heat. Stir in the parsley green onion purée. Add freshly ground black pepper, another teaspoon of salt, or more or less to taste.