Wash and dry all produce. Lightly oil a baking sheet and place in oven on upper rack. Preheat oven to 450 degrees. Halve tomatoes. Halve and peel shallot, then finely chop. Pick parsley leaves from stems. Finely chop leaves and stems, keeping them separate. Pick 1 tsp thyme leaves; reserve sprigs.

Halve potatoes lengthwise. Toss with a large drizzle of olive oil and season with plenty of salt and pepper. Carefully remove sheet from oven and arrange potatoes on it cut-side down, keeping them toward one side of sheet. Nestle half the thyme sprigs amongst potatoes (use the rest as you like). Roast in oven 10 minutes.

After 10 minutes, remove potatoes from oven and flip, keeping toward one side of sheet. Toss broccoli with a drizzle of olive oil, salt, and pepper and arrange on other side of sheet. Return to oven and roast until potatoes are tender and broccoli is beginning to char at edges, about 20 minutes more.

Meanwhile, put pine nuts in a large pan and place over medium-high heat. Toast, tossing often, until golden, 3-5 minutes. Transfer to a small bowl. Heat a drizzle of oil in same pan over medium-high heat. Pat steak dry with a paper towel. Season with plenty of salt and pepper. Add to pan and cook to desired doneness, 3-6 minutes per side. Remove from pan and set aside to rest on a plate. Wipe out pan.

Place same pan over medium-high heat. Add shallot and a drizzle of olive oil. Cook until softened, 1-2 minutes. Stir in demi-glace, tomatoes, and 1/2 cup water. Bring to a simmer, then remove from heat. Stir in reserved thyme leaves, half the parsley leaves, and 2 TBSP plain butter. Season with salt and pepper. Stir in any juices released by steak. Once done, remove potatoes and broccoli from oven. Heat broiler to high.

In a large bowl, toss potatoes with garlic herb butter and parsley stems. Sprinkle Parmesan over broccoli on sheet. Place under broiler to melt, 2-3 minutes. Divide steak, potatoes, and broccoli between plates. Sprinkle pine nuts over broccoli. Spoon sauce over steak. Top with rest of parsley leaves.