Pat the chicken thighs dry with paper towels. Sprinkle paprika, garlic powder, black pepper, salt, and dried thyme evenly over both sides of the chicken, rubbing the seasonings in well. This ensures the chicken tastes flavorful throughout roasting, not just from the glaze.

Spread baby potatoes and carrot slices on a large baking sheet. Drizzle with olive oil and toss to coat. Arrange them to create space in the center where the chicken thighs will sit, allowing everything to roast evenly.

Preheat oven to 400 degrees Fahrenheit. Place seasoned chicken thighs skin-side up in the center of the baking sheet, nestled among the potatoes and carrots. Roast for 15 minutes to crisp the chicken skin and soften the potatoes slightly.

While chicken roasts, whisk together honey, soy sauce, minced garlic, and melted butter in a small bowl until smooth. After the initial 15 minutes, brush this glaze generously over the chicken thighs.

Scatter broccoli florets and corn kernels around the baking sheet with the chicken and other vegetables. Toss them gently with the pan drippings and glaze to coat, then return the sheet to the oven.

Bring water to a boil and gently add eggs. Cook for 6 to 7 minutes for soft-boiled eggs with runny yolks. Alternatively, soft scramble them in a small pan with a touch of butter over low heat.

Continue roasting for another 15 minutes until the chicken skin is golden and crispy, potatoes are tender, and all vegetables are cooked through. The glaze should be sticky and caramelized. Let cool for 2 to 3 minutes, then transfer chicken, potatoes, carrots, broccoli, and corn to serving plates. Arrange halved soft-boiled eggs on the side and spoon any pan drippings over the top.