Combine artichoke hearts, smashed garlic, 2 tablespoons olive oil, and lemon juice in a bowl. Season with salt and pepper. Refrigerate for up to 1 day, then discard the garlic.

Cook sugar snap peas in boiling water for about 5 minutes until tender. Transfer to a colander under cold running water and drain.

Cook fava beans in boiling water for 2 minutes. Peel and add to the sugar snap peas.

Heat a skillet and add artichokes in a single layer. Cook over high heat, turning occasionally, until golden, about 8 minutes. Transfer to a large bowl.

Add sugar snap peas and fava beans to the skillet and cook for 3 minutes. Add to the artichokes.

Cook cavatappi pasta in boiling salted water until al dente. Drain well, reserving 1/2 cup of the cooking water.

Add the pasta to the vegetables.

Heat remaining 3/4 cup olive oil in the skillet. Add chiles and sliced garlic and cook over high heat, stirring, for 2 minutes.

Add shrimp, scallions, and tarragon. Season with salt and pepper and cook, stirring, until the shrimp turn pink.

Add white wine and cook, stirring, for 2 minutes.

Pour over the pasta and toss. Add some of the reserved cooking water if the pasta looks dry. Season with salt and pepper and serve.