Preheat your oven to 425°F. While it heats, slice your potatoes into thin ⅛-inch slices—I find the easiest way is to place a wooden spoon on either side of the potato as you slice; it acts as a guide and prevents you from cutting all the way through, keeping the potato intact at the base. Arrange the sliced potatoes on a baking sheet, drizzle generously with olive oil, and season with salt and pepper. Roast for 45-55 minutes until the potatoes are tender and the edges begin to crisp slightly.

While the potatoes roast, melt the butter in a small saucepan over medium-low heat. Add the minced garlic, sage, and thyme, stirring gently for about 1-2 minutes until fragrant—don't let the garlic brown or it will turn bitter. Season with salt and pepper, then remove from heat and set aside. This aromatic butter will infuse and cool slightly while you wait for the potatoes.

Remove the partially roasted potatoes from the oven and carefully brush the garlic herb butter mixture from Step 2 over the top and between the slices. Stuff the cheddar cheese between the potato slices, distributing it evenly across all potatoes, then generously sprinkle the freshly grated Parmesan on top. I like to use freshly grated Parmesan here because pre-grated cheese contains anti-caking agents that prevent it from melting as smoothly. Return to the oven and roast for another 25-35 minutes until the cheese is melted and bubbly, and the potatoes are golden and tender.

Remove the hasselback potatoes from the oven and let them cool for 2-3 minutes. Garnish generously with fresh sliced chives just before serving for a bright, onion-like freshness that cuts through the richness of the butter and cheese.