Bring a medium sauce pot of generously salted water to a boil. Add the farfalle and cook until tender, 10 to 12 minutes. Drain and set aside.
While the water heats and the farfalle cooks, prepare the squash.

• Trim the ends from the summer squash; cut the squash in half lengthwise.

In a medium bowl, toss the squash with 2 tablespoons oil and season with salt and pepper.
In a large grill or frying pan over high heat, cook the squash, cut side down, until charred, 3 to 5 minutes. Transfer the squash to a cutting board to cool slightly, then cut crosswise into ¼-inch-thick half-moons.
While the squash cooks and cools, prepare the remaining vegetables.

• Peel and thinly slice the yellow onion.
• Cut the cherry tomatoes in half.
• Finely chop, press, or grate enough garlic to measure 1 teaspoon.
• Remove the stem, ribs, and seeds from the bell pepper. Thinly slice the bell pepper.
• Cut the snap peas in half crosswise on the diagonal.
• Strip the basil leaves from the stems; coarsely tear the leaves.
• Strip the parsley leaves from the stems; coarsely chop the leaves for garnish.

In a large frying pan over medium-high heat, warm 2 tablespoons oil until hot but not smoking. Add the onion, season with salt and pepper, and cook, stirring occasionally, until just starting to brown, 3 to 5 minutes. Stir in the tomatoes and garlic and cook until fragrant, about 1 minute. Add the bell pepper, snap peas, and basil and cook, stirring occasionally, until the bell pepper and snap peas are crisp-tender, 2 to 3 minutes.
Stir in the farfalle and squash and toss to combine. Stir in the yogurt and 1 tablespoon butter, if using, and heat until blended, about 1 minute.
Remove from the heat, stir in the Parmesan, and season to taste with salt and pepper.

Transfer the farfalle and vegetables to individual bowls, garnish with the parsley, and serve.