Wash and dry all produce. Adjust rack to middle position and preheat oven to 400 degrees. Cut sweet potatoes into 1/2-inch cubes. Strip thyme leaves from stems; discard stems. Finely chop leaves.

Toss sweet potatoes on a baking sheet with half the thyme, a large drizzle of olive oil, and a pinch of salt and pepper. Roast in oven until tender and crisped, about 25 minutes total (we’ll check on them after 10 minutes).

Once sweet potatoes have roasted 10 minutes, give them a toss and push toward one side of sheet. Add green beans to same sheet and toss with a large drizzle of olive oil. Season with salt and pepper. Return to oven and roast until green beans are tender and potatoes are done, about 15 minutes.

Meanwhile, heat a large drizzle of olive oil in a large pan over medium-high heat. Season steak all over with salt and pepper. Add to pan and cook to desired doneness, 3-6 minutes per side. Remove from pan and let rest 5 minutes.

Add demi-glace, 1/4 cup water, and remaining thyme to same pan over medium-high heat and stir, scraping up any browned bits from bottom. Let simmer until thickened, 1-2 minutes. Remove from heat and add 1 TBSP butter, stirring or swirling pan to melt. Season with salt and pepper.

Sprinkle almonds over green beans and sweet potatoes on baking sheet. Thinly slice steak against the grain. Divide green beans, sweet potatoes, and steak between plates. Drizzle with pan sauce and serve.