Prepare the squash: Preheat the oven to 425°F and line a baking sheet with parchment paper. Wash the delicata squash, trim the ends, and slice in half lengthwise. Scoop out the seeds, then cut into ½-inch-thick half-moons. There is no need to peel the squash, as the skin is edible.
Season the squash: Arrange the squash on the prepared baking sheet and toss with olive oil, honey, smoked paprika, salt, and pepper until evenly coated. Spread into a single layer, making sure the pieces aren't overcrowded.
Roast the squash: Roast for 25–30 minutes, flipping halfway through, until the squash is tender and golden around the edges. Keep an eye on it toward the end since the honey can caramelize quickly.
Make the whipped feta: While the squash roasts, add the feta, Greek yogurt, olive oil, lemon juice, lemon zest, garlic, and black pepper to a food processor. Blend until smooth and creamy, scraping down the sides as needed. If the mixture is too thick, add a small splash of water or additional olive oil until it reaches a spreadable consistency.
Assemble the dish: Spread the whipped feta evenly across the bottom of a shallow serving plate or platter. Arrange the warm roasted delicata squash over the feta, slightly overlapping the pieces.
Garnish and serve: Drizzle with additional honey and finish with roughly chopped pistachios for a little crunch. Serve with crackers or crispy bread while the squash is warm.