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Bring a 5-quart stockpot over high heat. Add the thawed peas, diced onion, minced parsley, olive oil, salt, and water. Bring everything to a boil.
Once boiling, add the thawed artichoke hearts. Reduce the heat to medium, cover the pot, and let it cook for about 20 minutes. After 20 minutes, turn off the heat but keep the lid on.
Let the peas and artichokes rest together, covered, for 30 to 40 minutes. This resting step is crucial — it allows all the flavors to marry.
While the peas and artichokes are resting, bring a medium pot of generously salted water to a boil. Add the ditalini and cook until al dente according to package instructions. Drain the pasta and toss it into the pot with the peas and artichokes, stirring gently to combine.
Drizzle with a little more extra-virgin olive oil just before serving. Serve warm in bowls.