How to Make It
Preheat broiler with oven rack 6 to 8 inches from heat. Place green beans and tomatoes on a large baking sheet. Drizzle with olive oil, and sprinkle with 1 teaspoon of the salt and 1/2 teaspoon of the pepper; toss well.
Broil for 5 minutes. Remove baking sheet from oven. Sprinkle steaks with remaining 1/2 teaspoon each salt and pepper. Arrange steaks on baking sheet in a single layer, moving green beans and tomatoes aside to make room.
Return baking sheet to oven; broil until steaks are desired degree of doneness, 2 to 4 minutes per side, for medium. Remove from oven; let steaks rest 5 minutes before slicing.
Combine butter, blue cheese, and thyme in a small bowl; stir well. Serve butter mixture over steaks.