Cut a small "x" in the bottom of the tomato. Bring a large pot of salted water to a boil over high heat. Add the tomato and cook it for 30 seconds. Remove it to a bowl of salted iced water. Add the asparagus in the boiling water and blanch for 1 minute. Remove the asparagus to the iced water bath to cool down, then drain both the tomato and the asparagus. Peel the tomato, remove the seeds, and roughly chop it. Cut the asparagus into 1-inch pieces and set aside.
In a large skillet over medium-high heat, add the olive oil. When the oil is hot, add the tomato, garlic, herbs, and lemon juice, and season with salt and pepper, to taste. Cook until the tomato begins to soften, about 5 minutes. Stir in the asparagus and cook until is just tender, about 2 to 3 minutes. Spoon the mixture into an ovenproof casserole and scatter with some Parmesan shavings. Bake until the cheese is melted and lightly browned, about 4 to 5 minutes. Remove from the oven and serve.