In a large cast iron or non stick skillet, heat the olive oil on medium high. Add the garlic and broccolini. Saute the broccolini until cooked through, but still firm. About 5 minutes. Season with a bit of salt and pepper.
Remove the broccolini from the pan, place in a bowl or on a plate and set aside.
Now, add the mushrooms to that same pan, if there is not enough residual oil in the pan, add a little more. Saute the mushrooms until they are cooked through. Reducing heat as needed. The mushrooms should release liquid. Cook them until the liquid has evaporated. This should take about 5 minutes. Season with salt and pepper. Reduce heat to low.
Now add the Marsala to the pan with the mushrooms, and deglaze the pan. Scraping any bits of mushroom off the bottom.
Now add the veggie broth and coconut milk. Cook the sauce for about 15 minutes until it has reduced by almost half. Taste and season to your liking.
Now add the broccolini back to the pan, and toss in the sauce. Just make sure the broccolini is nice and hot, then serve immediately with pasta, polenta, quinoa or whatever your heat desires!