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Place oven rack in center position and pre-heat oven to 350°F.
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Melt one tablespoon oil in a large, high-sided skillet over medium heat. Add the mushroom and shallots and season with salt and black pepper, to taste. Cook, stirring occasionally until the mushrooms and shallots develop a bit of color and soften, approximately 4-5 minutes. Remove from heat and transfer to a bowl and set aside.
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Melt the remaining oil in a small bowl in a microwave. Add the rosemary and garlic to the coconut oil and season with salt and black pepper, to taste. Rub the rosemary-garlic mixture on top and all along the sides of the beef.
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Arrange the sliced red onion on the bottom of the same skillet and place the seasoned beef tenderloin on top of the onions.
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Arrange the mushroom and shallot mixture around the sides of the beef and place in the pre-heated oven for 45-50 minutes for medium-rare or longer for more well done results.
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Remove from oven and rest for 10-15 minutes before serving. Enjoy!