Cover potatoes with cold water in a pot, add 1 tsp salt, and bring to a boil.
Simmer until fork-tender, 12–15 minutes. Drain well and return to the warm pot to steam off moisture.
Mash potatoes with butter, warm milk, and garlic until smooth and creamy.
Stir in remaining salt, black pepper, smoked paprika, and cornstarch until fully absorbed.
Fold in cheddar, Parmesan, and parsley. Let cool 10 minutes; chill 20 minutes if the mixture feels soft.
Scoop heaping tablespoon portions and roll into 1-inch balls with lightly oiled hands.
Roll each ball in panko, pressing gently so crumbs adhere on all sides.
Heat oil in a deep skillet to 350°F. Fry pops in batches, turning as needed, until golden and crisp, 3–4 minutes.
Drain on a rack or paper towels and season lightly with salt. Serve hot with your favorite dip.