Preheat your oven to 400°F. While it heats, trim the tough woody ends off the asparagus (about the bottom inch or so), leaving spears about 5 inches long. Toss the trimmed asparagus on a baking sheet with olive oil and salt, spreading them in a single layer. Roast for 10 minutes until they're tender-crisp but still have a slight bite—this partial cooking ensures they're perfectly done inside the pastry without becoming mushy.
While the asparagus roasts, unroll your crescent roll pastry and separate it into individual triangles along the perforated lines. Lay the triangles out on a clean work surface. Shred your cheddar cheese if not already done. In a small bowl, combine the melted and slightly cooled butter with the bagel seasoning—I find letting the butter cool just a bit prevents it from soaking through the delicate pastry too quickly.
Once the roasted asparagus from Step 1 is done, remove it from the oven and let it cool for just 1-2 minutes so you can handle it. Working with one crescent triangle at a time, sprinkle about 1 tablespoon of cheddar cheese onto the wider base of the triangle. Place 3 asparagus spears on top of the cheese with the tips pointing toward the narrow end of the triangle. Roll up the pastry tightly from the wide end toward the point, tucking the asparagus tips into the roll as you go. Arrange the completed rolls seam-side down on a clean baking sheet.
Brush each assembled roll generously with the butter and bagel seasoning mixture from Step 2, coating both the top and sides—this creates a beautiful golden crust and adds incredible flavor. Bake at 400°F for 15-18 minutes until the pastry is deeply golden brown and puffed. The rolls should be crispy on the outside and the asparagus perfectly tender inside.