Preheat your oven to 450°F. While it heats, wash the asparagus and trim about 1 inch off the woody bottom ends. Pat dry with paper towels—this helps them roast instead of steam. Toss the asparagus with olive oil, salt, pepper, lemon juice, and a pinch of red pepper flakes. Spread them in a single layer on a sheet pan and roast for 10 minutes until tender-crisp with slight browning. The asparagus should still have a bit of firmness so it won't get mushy when grilled.

While the asparagus roasts, lay out all 4 bread slices on a clean work surface. Spread room-temperature butter on one side of each slice—the butter should spread easily without tearing the bread. On the non-buttered side of 2 bread slices, spread 3/4 tablespoon pesto each, then layer with about 2.5 oz of the thick cheddar slices. Once the asparagus is done roasting, divide it evenly between these two slices, arranging the spears in a single layer. Top each with the remaining 2 bread slices, buttered side facing outward.

Heat a skillet over medium heat for about 1 minute until it's evenly warm. Place both sandwiches in the skillet and cook for 3-5 minutes until the bottom is golden-brown and crispy. I like to press down gently with a spatula for the first minute to encourage even contact with the pan and help the cheese melt faster. Carefully flip each sandwich and cook the other side for another 3-5 minutes until golden and the cheese is fully melted. Transfer to a plate and serve immediately while the cheese is still warm and gooey.