In a large, dry skillet, toast 1 cup of the seeds over medium-low heat until golden and fragrant, about 8 minutes, stirring occasionally. Remove and let cool. Add the tomatillos, onions and garlic to the skillet and cook over medium-low heat until the skins are slightly charred, 8 to 10 minutes, stirring occasionally. Remove from the heat and let cool slightly.
In a medium pot, combine the potatoes and 1 teaspoon salt with enough water, to cover. Bring to a boil and simmer until tender. Drain.
In a second pot, combine the green beans and remaining teaspoon of salt in water to cover. Bring to a boil and simmer until tender. Drain, reserving 1/2 cup of liquid.
To make the sauce, pulse the roasted squash seeds in a blender or food processor. Add the tomatillo mixture and the 1/4 cup of the reserved string bean cooking liquid. Puree on high speed until smooth, adding more reserved cooking liquid as needed. Season, to taste, with pepper and cayenne. Strain the sauce through a medium strainer.
Combine the cooked potatoes and green beans in a bowl. Toss with the sauce and remaining 1/2 cup of nuts, and refrigerate for 1 hour before serving. Serve chilled.