Fill a large pot with water and generously salt. Bring to a boil.
Quarter the potatoes, keeping all the pieces about the same size. Cut the stems off the green beans and cut into bite-sized pieces. Add the pasta and potatoes to the boiling, salted water.
Crush the garlic clove with a mortar & pestle. Add the basil leaves and crush until they form a paste. Then add sunflower seeds and continue to crush.
After the pasta & potatoes have boiled for 5 minutes, add the green beans.
Grab the olive oil and add a few glugs at a time to the mortar. Stir and smear to combine. Grate the parmesan into the mortar and stir until you get a creamy consistency.
Toss the butter into a large bowl. Strain the pasta and veggies through a colander. Add half the pasta and veggies to the bowl with butter. Add half the pesto to the bowl as well. Toss until well combined. Serve on a dinner plate with a drizzle of olive oil & garnish with more parmesan.