Preheat the oven to 350ºF and line two rimmed baking sheets with parchment paper.
Combine the asparagus, artichoke hearts, and sliced tomatoes in a large bowl and toss with the melted coconut oil. Arrange the vegetables in a single layer on the lined baking sheets, sprinkle with sea salt, and roast in the oven until tender, about 30 minutes. Remove from the oven and allow the vegetables to cool slightly.
To prepare the vinaigrette, combine the vinaigrette ingredients in a high-speed blender and blend until completely smooth. Set aside.
Place the chopped romaine in a large serving bowl and top with the warm roasted vegetables, roasted pepper, and chopped avocado. Pour the dressing over the top and toss well to coat. Serve immediately.