Make the Pumpkin Cream Cold Brew: In a small bowl or jar, mix the pumpkin puree, heavy cream, maple syrup, and pumpkin pie spice. Stir or whisk until smooth. Add the cold brew coffee to a glass filled with ice. Pour the pumpkin cream mixture over the cold brew, and stir to combine. Set aside.
Add the olive oil in a skillet over medium heat and sauté the sausage until nicely browned, add the sliced mushrooms until they are golden brown and tender, about 3-5 minutes.
Add the broccoli florets and sauté for 2-3 minutes until they are slightly tender.
Pour the beaten eggs tilting the skillet to ensure the eggs cover the bottom evenly.
Allow the eggs to cook for a few minutes until the edges start to set.
Sprinkle the shredded cheese over the omelet. Season with salt and pepper.
Fold the other half of the omelet over the filling and let it cook for another 2-3 minutes until the cheese melts and the eggs are fully cooked. Place the sliced avocado over top.
Slide the omelet onto a plate and serve immediately alongside the pumpkin cream cold brew.