Heat oil in large frying pan over medium-high heat. Add carrots and onion wedges, cut-side down. Reduce heat to medium and cook without stirring until veggies begin to caramelize, about 5 minutes. Turn to brown the other side and cook an additional 5 minutes.
Add greens and stock to the pan, bring to a simmer and cook 10 minutes.
Divide pieces of broken bread between two large soup bowls.
Spoon veggies over the top of the bread and then ladle broth over the bread.
Top with a fried or poached egg and drizzle a teaspoon or so of the red wine vinegar over the egg. Dust with freshly grated black pepper and serve.