Preheat oven to 375F (190C).

Toss asparagus tips with olive oil, fresh rosemary, salt, and pepper.

Spread asparagus on a cookie sheet.

Roast for 10 minutes.

In a wide, shallow dish, whisk together eggs, half-and-half, Parmesan cheese, salt, and pepper.

Dip one slice of bread in the egg mixture, soaking both sides.

Flip the bread over and press 4 roasted asparagus tips into the soaked bread in alternating directions.

Melt 2 teaspoons of butter in a skillet over medium-low heat.

Place 2 slices of bread, asparagus side down, into the skillet.

Cook slowly for about 4 minutes per side, pressing down occasionally to ensure good contact and browning.

While cooking the second side, sprinkle the asparagus side of each slice with a teaspoon or so of grated Parmesan cheese.

Keep warm in a 200F (93C) oven while preparing the second batch.

Serve hot with tomato jam (optional).