Preheat Your Oven: Preheat your oven to 375°F (190°C).
Prepare the Baking Sheet: Spread 1 ½ tablespoons of olive oil evenly on a half sheet pan.
Roast the Carrots: Slice the carrots in half lengthwise and arrange them in a single layer on the prepared baking sheet. Drizzle the remaining 1 ½ tablespoons of olive oil over the carrots and toss to coat. Sprinkle with kosher salt, cracked black pepper, and dried basil.
Bake the Carrots: Roast for 25-30 minutes, or until the carrots are tender-crisp and slightly firm when pierced with a fork.
Make the Balsamic Glaze (Or skip this step and use store bought Balsamic Glaze if you have it): While the carrots are baking, prepare the balsamic glaze. In a small saucepan or skillet, combine the balsamic vinegar, brown sugar, and butter. Cook over medium to medium-high heat for about 5 minutes, stirring occasionally, until the glaze has thickened slightly. Set aside.
Add Blue Cheese and Melt: Once the carrots are roasted, transfer them to an oven-proof serving dish. Sprinkle the crumbled blue cheese evenly over the warm carrots. Return the dish to the oven for an additional 3 minutes or until the blue cheese begins to melt and soften.
Garnish and Serve: Remove the carrots from the oven and sprinkle the toasted pepitas over the top. Drizzle generously with the prepared balsamic glaze. Serve immediately and enjoy this flavor-packed side dish!