Preheat the oven to 425°F.
Wash the beet and pierce it on all sides with a fork. Place the beet in the center of a piece of tin foil and drizzle with 1/2 teaspoon of the olive oil. Sprinkle with 1/4 teaspoon of the salt and wrap the tin foil around the beet so it is fully encased.
Place the beet on a baking sheet to catch any drips and place in the oven. Roast for 40 minutes or until tender. Remove the beet from the oven and let cool. When cool enough to handle, peel and cut into cubes. Transfer the beet to the fridge to cool completely.
Pour the wild rice, water, and 3/4 teaspoon of the salt into a medium saucepan. Place the pan over high heat and bring to a boil. Cover the pot and reduce to a low simmer. Let cook for 40 minutes or until the grains of rice split. There may be some residual moisture in the pot, so drain the rice using a fine mesh strainer. Fluff the rice and set aside to cool completely.
When everything is cool, place the rice, roasted beet, cucumber, pecans and goat cheese in a large bowl. Set aside.
In a small bowl, whisk the remaining olive oil, the remaining salt, the balsamic vinegar, garlic and mustard together. Pour the mixture over the salad and toss to coat.
Chill the salad until ready to serve.