How to Make It
Preheat oven to 400°F.
Place asparagus on a baking sheet; toss with 1 1/2 teaspoons oil. Roast at 400°F for 12 to 15 minutes or until crisp-tender, stirring twice. Remove from oven; cool on pan 10 minutes. Transfer to a bowl. Cut 1 cup of tomatoes in half lengthwise (through the stem end), and place in bowl with asparagus and 2/3 cup walnuts; toss gently to combine.
Place remaining tomatoes in a small saucepan with 3 tablespoons water, anchovy, and remaining 1 1/2 tablespoons oil. Cover and bring mixture to a boil over medium-high heat. Reduce heat to medium-low, and simmer 12 minutes or until tomatoes burst. Remove pan from heat; cool slightly (about 5 minutes). Transfer tomato mixture to a food processor or blender; add salt, pepper, and remaining walnuts. Process until smooth. Pour over asparagus mixture, and toss to coat. Let stand at room temperature 15 to 30 minutes for flavors to mingle. Arrange on a serving platter; sprinkle evenly with cheese.