- Make the squash: Light a Big Green Egg or large grill to a medium flame. Peel squash and slice into 1-inch thick rounds. Coat rounds in oil and season with salt and pepper. Place rounds on grill and cover. Turn occasionally and cook until rounds are soft to the touch, about 6 minutes per side.
- Make the roast: Season roast with salt and pepper. Place roast on grill grates and cook for about 20 to 35 minutes, turning as needed and closing lid between turns. Cook until internal temperature reaches 119 degrees. Remove from grill and let rest for 15 minutes for medium rare.
- Make the béarnaise: In large saucepan over low heat, add vinegar and tarragon. Cook for 5 minutes. Remove from heat and let cool to room temperature. Make a double boiler by heating a medium-sized pot fi lled halfway with water over low heat and placing a large bowl over top, making sure the bowl does not touch the water. In bowl of double boiler, combine egg yolks and vinegar and whisk until thick. Add butter a tablespoon at a time, stirring until melted. Season with salt to taste.
- To serve, spoon béarnaise over top or alongside the strip roast and squash.