Position the oven racks in the top and bottom thirds of the oven; preheat to 425°. Line 2 baking sheets with parchment paper. In a large bowl, toss the fennel with about 1 tbsp. oil, a large pinch of salt, and pepper. Arrange on one of the baking sheets in a single layer. Repeat the process with the cauliflower. Roast the fennel and cauliflower, rotating the pans halfway through roasting, until golden and tender, 15 to 25 minutes. Repeat the process with the Brussels sprouts on one baking sheet and the celery and squash on the second sheet.
Meanwhile, in a small saucepan, melt the butter over medium heat, swirling occasionally, until it begins to bubble, about 2 minutes. Cook, swirling constantly, until the bubbles subside, about 1 minute. Reduce the heat to low and cook, continuing to swirl, until the bubbles disappear and the butter is golden brown and smells nutty, about 1 minute more. Transfer to a bowl.
Toss the roasted vegetables with the brown butter, parsley, and vinegar. Season. Spread the freekeh on a platter. Top with the roasted vegetables.