Bring a medium sauce pot of generously salted water to a boil. Separate the pappardelle so the noodles don’t clump together during cooking. Add the pappardelle and cook, stirring occasionally, until just tender, 3 to 5 minutes. Drain the pappardelle, reserving ¼ cup [½ cup] pasta cooking water. 

While the water is heating and the pappardelle is cooking, prepare the vegetables. 

• Trim the stem ends from the maitake mushrooms; cut the mushrooms into 1-inch slices.
• Trim the root ends from the baby broccoli; cut the broccoli into 2-inch lengths.
• Scrape off any seeds from the roasted red peppers; coarsely chop any large pieces.

In a large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the mushrooms, season with salt and pepper, and cook, undisturbed, until starting to brown on one side, 3 to 5 minutes. Add the broccoli, season with salt and pepper, and cook, stirring occasionally, until the mushrooms are tender and the broccoli is lightly browned and crisp-tender, 2 to 3 minutes.

• Check the olives for any pits.

To the pan with the vegetables, stir in the roasted red peppers and olives and cook until warmed through, about 1 minute. Stir in the pappardelle, reserved pasta cooking water, and pesto and toss to coat. Cook until warmed through, about 1 minute. Remove from the heat and season to taste with salt and pepper.