Preheat the oven to 400°F.
Cut just the tips of the broccolini heads off. Scatter them on a baking sheet. Cut the stems into 1" pieces and scatter them on a separate baking sheet. Drizzle the broccolini heads with a bit of olive oil and season with a pinch of salt. Toss to coat. Don't add anything to the broccolini stems.
Add the broccolini heads to the top rack of your oven and the stems to the bottom. Roast the heads for 10 minutes or until slightly crisp, and roast the stems for 20 minutes or until they are cooked but not losing their color.
While the broccolini is roasting, add the sunflower seeds to a heat-proof bowl or cup. Pour boiling water over them and let them sit for 5 minutes.
Add the basil, anchovies, spinach, lemon juice, and 1/8 tsp of kosher salt to a food processor. When the sunflower seeds are softened, drain them and add them in as well. Process for an extended amount of time, about 2-3 minutes, drizzling in the olive oil gradually. Scrape down the sides and repeat until the mixture starts to become spreadable. If needed, you can add up to 1/4 cup of water to help the process.
When the broccolini stems are out of the oven, let them cool to room temperature. Add them into the food processor and process until you form a thick spread. It won't be completely smooth, but the texture is still delicious. Taste and season with salt and lemon juice as needed.
To serve, spread a generous helping of the broccolini spread on each slice of bread. Add the broccolini heads on top and dot with the chili oil. Top with the pecorino romano and eat immediately!