Preheat your oven to 350°F so it's ready the moment your tray is prepped. While it heats, cube your pumpkin into even 1.5-inch pieces so everything roasts at the same pace. I also pat my chicken breasts dry with a paper towel here, which helps them brown instead of steam in the oven.
Add the balsamic vinegar, honey, olive oil, salt, and pepper into your jar, screw the lid on tight, and give it a good shake until it's fully combined. I like making this first so the flavors have time to meld while everything else cooks. Set it aside on the counter.
Place your cubed pumpkin in a mixing bowl with the olive oil, salt, and pepper, then toss until every piece is coated. Scatter it out in a single layer on your baking sheet so it roasts instead of steams. Give the pieces a little breathing room between them.
In the same bowl, add your chicken breasts with about a tablespoon of the dressing you just shook up. Turn the chicken to coat it evenly, then nestle it onto the same tray as the pumpkin. This is the step that makes the whole thing so efficient.
Slide the tray into the oven and roast for 25 minutes, flipping the pumpkin around the 15-minute mark so it browns evenly on both sides. You're looking for pumpkin that's fork-tender and chicken that's cooked through with a nice golden color on top.
Pull the tray out and let the chicken rest for a couple of minutes before roughly chopping it into bite-sized pieces. Resting keeps the juices inside instead of running out onto your cutting board. I usually use this time to start toasting my pine nuts.
Add the pine nuts to a dry skillet over medium heat and toast them, shaking the pan often, until they're golden brown. This only takes a couple of minutes, and they burn fast, so don't walk away. Remove them from the heat the second they're done.
In your large salad bowl, toss the arugula and chopped chicken with a bit of dressing first, then transfer it to your serving dish. Scatter the warm pumpkin over the top, crumble on the feta and pine nuts, and finish with the remaining dressing before serving right away.