Rinse the radishes thoroughly under cold water to remove any dirt. Trim both ends, then slice them into quarters.
Place a large skillet over medium-high heat. Add the oil and butter, let them melt together, and swirl the pan to coat it evenly.
Add the radishes to the hot skillet in a single layer. Sauté, stirring occasionally with a spatula. After about 8-10 minutes, check for color—the edges should start turning golden and crisp.
Continue cooking until the radishes are fork-tender inside and crispy on the outside, about another 5–7 minutes. Taste one for texture. It should have a slight crunch but yield easily when pierced. If needed, cook a bit longer until you achieve your desired crispiness.
Remove the skillet from the heat. Transfer the radish fries to a plate lined with paper towels to drain off excess oil. Sprinkle the fries with salt and pepper to taste, tossing to coat evenly. Serve hot with an optional garnish of fresh herbs or grated Parmesan cheese.