Mise en place -Slice the chorizo into quarters lengthwise, then chop into bite-sized pieces. Peel and dice the onion. Trim and finely chop the celery. Chop enough parsley, stems and leaves, to yield about a ΒΌ cup.
Soften the veg - Melt the butter in a large pan, then add the chorizo, onion, and celery. Cook over low heat, stirring constantly, until the chorizo begins to render and the vegetables are very soft.
Build the broth and simmer - Stir in the tomato paste and parsley, then pour in the chicken stock. Stir gently. Season with salt and pepper, then bring to a boil. Cover, lower the heat, and simmer for ten minutes or so.
Drop the pasta - When ready, drop the pasta into the broth and stir. Bring to a boil and simmer until the pasta is tender, about 10 minutes. Remove from the heat, stir in the peas, and cover until the peas are thawed and warmed through.
Serve - Serve hot with grated Parmesan at the table.