In a 4-quart soup pot or large sauce pan, add the potatoes and parsnips and cover with cold water one inch above vegetables. Bring to a boil, reduce heat to medium-low and simmer until potatoes and parsnips are tender (until a paring knife slips in and out of veggies easily), about 20 minutes.
Meanwhile, melt the butter in a small saucepan over medium-low heat. Add the minced garlic, reduce heat to low and let cook, stirring often, until garlic begins to turn golden brown, about 12-14 minutes. Remove pan from heat and set aside for 5 minutes. The garlic will continue to brown. Pour mixture through a fine-mesh strainer into a small bowl and set aside toasted garlic. Also, heat the milk in a small pan over low heat.
Drain the potatoes and parsnips in a colander. Place the potatoes and parsnips back into the pot and put back on the burner with the heat turned off. Using a potato masher, mash them until they are free of all lumps.
Add the strained butter to the potato/parsnip mixture and mix until just incorporated . Add the warmed milk a little at a time and beat with a wooden spoon until you reach your desired consistency. Add salt, pepper and chives and gently stir to combine. Garnish with toasted garlic and serve immediately.