Gather a medium mixing bowl, a large frying pan, a spatula, a slotted spoon, and a paper towel-lined plate. Prepare your cooked mashed potatoes, grated carrots, sautéed onion, roasted garlic, and chopped herbs nearby.
Add the mashed potatoes and grated carrots into the bowl and mix until well combined and smooth.
Stir in the sautéed onion, mashed roasted garlic, and chopped herbs, ensuring everything is evenly distributed for a fragrant, colorful mash.
If the mixture feels loose or too soft, sprinkle in a few tablespoons of panko breadcrumbs and fold until it holds together firmly enough to shape.
Using about 2 tablespoons of the mixture, gently roll it between your palms to form small rounds or logs, placing each on a tray or plate for shaping.
Set up two shallow dishes: one with the beaten egg and another with the toasted panko breadcrumbs. Dip each croquette into the egg, allowing excess to drip off, then coat thoroughly in the breadcrumbs.
Heat enough neutral oil in a large frying pan over medium-high heat until it reaches about 180°C (356°F)—test by dropping a breadcrumb; it should sizzle immediately.
Carefully place a few croquettes into the hot oil, frying in batches to avoid overcrowding. Cook for 3-4 minutes, turning gently with a spatula, until they are golden, crispy, and bubbling.
Using a slotted spoon, transfer the fried croquettes onto the paper towel-lined plate to drain excess oil. Rest for a minute to set the crust and keep the croquettes crispy.
Repeat with remaining croquettes, maintaining the oil temperature, until all are golden and crispy.
Serve the croquettes warm, garnished with extra herbs if desired, alongside your favorite dip or a squeeze of lemon for added brightness.