Position a rack in the center of the oven and preheat to 375 degrees . In a large pot filled halfway with boiling, lightly salted water, cook the potatoes for 3 minutes. Drain and spread evenly on a paper-towel-lined baking sheet to cool.
In a saucepan, melt the butter over medium heat. Add the chopped onion and cook, stirring, until softened, 3 minutes. Whisk in the flour for 2 minutes, then pour in the half-and-half and bring to a boil, whisking constantly; cook for 1 minutes. Remove from the heat. Stir in the cheese, 1 tsp. salt and 1/2 tsp. pepper. Let cool.
Using a food processor, chop the remaining onion and the carrots. Transfer to a bowl. Add the beet to the processor and chop. Transfer to a kitchen towel, wrap and squeeze out any excess moisture.
Whisk the eggs, marinara, breadcrumbs, 1 1/4 tsp. salt and 1/2 tsp. pepper into the carrot mixture. Crumble in the turkey, beef and beets and mix well. Transfer to a 9-by-13-inch oval casserole, pressing into an even layer. Top with the potatoes and cheese sauce.
Place the casserole on a baking sheet and bake until the edges are bubbly and the top is browned, about 40 minutes. Cover with foil and continue cooking until a meat thermometer placed in the center of the loaf registers 175 degrees , 20 to 25 minutes. let cook for 20 minutes before serving.
Puree the basil, EVOO, lemon juice and 1/2 tsp. salt. Serve with the meatloaf.