Add broccoli florets to a food processor and pulse until finely chopped but not mushy. You will still have some small chunks of broccoli visible. In the order listed, add ingredients to a blender: coconut milk, tahini, nutritional yeast, miso, sea salt and pepper. Puree until smooth.
Heat a large, straight-side skillet or pot to medium-low and add olive oil. When oil moves quickly around the pan, add shallots. Cook, stirring once or twice, until softened and translucent, approximately 4-5 minutes.
Add broccoli to the skillet, along with the liquid mixture. Stir carefully to incorporate, then turn heat to medium and bring to a simmer. Simmer for approximately 10 minutes, until thickened and no liquid remains around the edges. Remove from the heat and stir in sun-dried tomatoes and fresh basil. Taste for more salt and serve immediately!
Leftovers will keep tightly sealed in the refrigerator up to 5 days. Allow to cool completely before sealing container to prevent condensation build up.