Bring a pot of water to a boil, add the sliced potatoes, and cook until fork-tender. This takes about 10 minutes.
In a separate pot, boil the chopped carrots until soft. Give them around 8 minutes, then drain both the potatoes and carrots and let them cool for a few minutes.
While the vegetables are cooling, finely chop the green onions and set them aside.
In a large bowl, mash the cooked potatoes with a fork or potato masher until mostly smooth.
Mash or finely grind the cooked carrots, then stir them into the mashed potatoes.
Add the chopped green onions, paprika, salt, and corn starch to the bowl. Mix everything together until it’s well blended and holds together nicely.
Spoon the mixture into a large zip-top bag, seal it tight, and snip off one bottom corner to make a simple piping bag.
Heat a thin layer of vegetable oil in a nonstick pan over medium heat until it starts to shimmer.
Pipe small rounds of the fritter mixture into the hot oil. Gently flatten each one with the back of a spoon. Cook each side for 2 to 3 minutes or until golden brown and crisp.
Remove the fritters from the pan and place them on a paper towel-lined plate to drain. Serve them hot and fresh, because that’s when they’re the absolute best.