Fold the potatoes into a large saucepan, add enough water, cover and bring to a boil over high heat. Reduce heat and simmer until soft, about 10 minutes. Drain the water and put the cream cheese and butter in a saucepan with potatoes. Mash potatoes well with a potato grinder.
Turn on the oven to preheat to 180 degrees. Lubricate with vegetable oil a heat-resistant form, about 25×35 cm in size.
Put sour cream, tarragon, cheddar cheese into the potato mass, pour milk and salt. Mix well.
Put the potato mass into the prepared dish and place in the preheated oven. Bake mashed potatoes for about 35-45 minutes. Let the potatoes stand at room temperature for 5-10 minutes before serving.