Add chopped potatoes to large pot. Fill pot with enough water that water sits 1" above top of potatoes. Add 1 to 2 pinches salt and stir to incorporate, then place pot on stovetop over medium-high heat.
Bring water to gentle boil. Boil 10 to 15 minutes or until potatoes can easily be pierced with tines of fork but not fall apart.
While potatoes boil, heat dutch oven over medium heat. When pot is warm, add putter and melt completely, moving butter around occasionally with large spoon to coat bottom of pot.
When potatoes are ready, remove 1 cup of water from boiled potatoes and transfer water to small bowl. Pour remaining water and potatoes through colander to drain, then set potatoes aside.
When butter is melted, add chopped onion. Sauté onion, stirring occasionally, until onions have softened. Be careful not to burn butter.
Remove pot with onions from heat. Add boiled potatoes, room-temperature milk, 1 teaspoon salt, and pepper to pot. Stir to incorporate, then return pot to heat.
Bring mixture to gentle simmer. Be careful not to boil milk - mixture should only develop small bubbles around edge of pot.
Let mixture simmer gently 10 minutes. After 10 minutes, remove pot from heat. Use potato masher or immersion blender to mash or purée approximately 50% of potatoes, leaving remaining potatoes chunky as desired.
If desired, stir in reserved liquid from boiling potatoes as needed to thin soup and achieve preferred consistency. Taste and adjust salt and pepper as needed, then portion into serving bowls and serve hot.