Irish Zucchini and Potato Pancakes

Ingredients

• 1 cup prepared mashed potatoes
• 1 cup all-purpose flour
• ¼ cup milk
• 1 egg
• 3 tablespoons unsalted butter, melted
• 2 teaspoons fine sea salt
• 1 ½ cups shredded Yukon Gold potatoes
• 1 cup shredded Cheddar cheese
• 1 small zucchini, shredded
• canola oil, or as needed, divided