Position a rack in the lower spot in the oven and another in the middle and preheat to 425º F. In a large bowl, toss the carrots, potatoes and shallots with 1 teaspoon salt (Diamond Crystal kosher but adjust based on your salt’s saltiness) and 2 tablespoons of the olive oil. Spread the vegetables on a parchment-lined sheet pan and place on the lower rack of the oven. Roast until golden to lightly brown and mostly cooked through but still al dente, about 20 minutes.
Meanwhile, season the sirloin tips in the vegetable bowl with salt and pepper and toss with the remaining 2 tablespoons of olive oil. Add the seasoned sirloin to the sheet pan and roast with the vegetables until browned all over and medium rare or 130º F with an instant read thermometer stuck into the thickest piece of sirloin, about 10 minutes. Take the sheet pan out and set on a cooling rack. Let cool for about 10 minutes before serving.
When ready to serve, drizzle as much yogurt on the sheet pan as you’d like; the same goes for the chili crisp. Then juice the lemon halves over everything.