Grilled vegetable hash with eggs

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I always thought of this as "standard stuff, nothing special", until I was chatting with a friend who wanted to know more. So I figured I'd share.

This is ideal for using up produce odds and ends. The only trick with ingredient changes is to vary when you add vegetables to the pan by how long they need to cook. Within type, making the pieces as uniform as possible helps.

Ingredients (for two people)

1 medium sweet potato (mine was a fingerling), diced
1 large carrot, diced
1/4 head cauliflower, cut into small florets and stems diced
1 large or two small shallots, chopped
3 sweet small (lunchbox) peppers, sliced (I used one each of red, orange, and yellow)
herbs and sea salt to taste (I used fresh dill this time; in the past I've used fresh or dried rosemary)
olive oil for roasting
6 medium eggs
butter for frying eggs

Instructions

These instructions are for a convection (fan) oven. If you don't have that, increase temperature by 25 degrees F and cook a little longer (you'll need to monitor it and decide when it's done).

Set oven to convection roast, 400 F.
In a shallow roasting pan, combine potato, carrot, cauliflower, and enough oil to coat. Roast for 15 minutes.
Add shallots, peppers, and seasonings, stir to coat, and return to oven for another 15 minutes.
Check after a total cooking time of 30 minutes. If you like your vegetables softer, cook a few minutes longer.
When the vegetables are done, melt butter in a skillet and transfer the vegetables to plates. Fry eggs -- sunny side up or over easy both work.
Put the eggs on top of the vegetables and eat immediately.