Step 1

Melt butter in a medium saucepan over medium-low heat, then simmer gently, reducing heat if needed and skimming foam from surface, until butter is no longer foaming and is beginning to brown, 10–15 minutes.

Step 2

Mix onion, thyme, ginger, garlic, cumin, oregano, and turmeric into brown butter and cook, stirring occasionally, until onion is golden brown and mixture smells very fragrant, about 15 minutes. Stir in berbere and cook, stirring constantly, just until the spice mixture is very fragrant, about 1 minute. Strain brown butter through a fine-mesh sieve into a small bowl and let cool completely; discard solids.Do ahead: Spiced brown butter can be made 1 week ahead. Cover and chill.

Step 3

Preheat oven to 400°. Place carrots on a large rimmed baking sheet. Drizzle 4 Tbsp. oil over, season with salt and pepper, and toss to coat. Add orange slices and gently toss again just to combine. Roast, tossing halfway through, until carrots are browned in spots and tender (they should be easy to pierce with a fork), 30–40 minutes. Let cool slightly.

Step 4

Meanwhile, whisk lemon juice, honey, mustard, remaining 2 Tbsp. oil, and 3 Tbsp. spiced brown butter (reheat if it has solidified) in a small bowl. This is your vinaigrette.

Step 5

To serve, transfer carrots to a platter. Drizzle vinaigrette over and top with parsley and ayib.