Preheat the oven to 375 degrees F (190 degrees C).

Individually wrap beets, onion, and garlic in aluminum foil. Place on a baking sheet.

Bake in the preheated oven until beets and onion are fork-tender, about 1 hour. Remove garlic after about 30 minutes. Let cool to room temperature.

Mix all-purpose flour, whole wheat flour, and salt in a large bowl. Make a well in the center and mix in eggs, gradually adding water until dough comes together.

Knead the dough on a work surface until smooth and elastic. Divide into 4 portions, wrap in plastic, and refrigerate at least 1 hour.

For filling: Peel the roasted beets, onion, and garlic. Combine with dill and goat cheese in a food processor. Pulse until smooth.

Roll dough through a pasta roller to 1/16-inch thickness. Cover sheets with a damp towel to keep from drying.

Lay a pasta sheet down, place teaspoon-sized portions of filling 3 inches apart, brush edges with water, and cover with another pasta sheet. Seal edges.

Cut ravioli with a 2 1/2-inch cutter and press the edges. Place finished ravioli on a floured baking sheet.

Boil ravioli in salted water in batches until they rise to the surface (3-5 minutes).