For the gravy
Squidge the mince, sea salt, Worcestershire sauce and mustard together in a bowl and form into 2 firm, flat, deep burger shapes
Now start to make the gravy. In a pan fry the onion in the butter until very soft and turning golden brown. Add the sugar and caramelize even more before stirring in the tomato purée. Stir, but allow this to catch a bit on the pan before adding the red wine vinegar and cooking for a further minute or so.
Pour in the consommé and wine and simmer rapidly until the appearance of the gravy is only just syrupy rather than wet (this will take about 10 minutes), then season to taste and turn off the heat.
In a medium nonstick frying pan, heat the sunflower oil enough that the burgers sizzle on entry and cook them to your desired doneness (about 4 minutes or so on each side over a medium-high heat).
Rest the burgers, briefly, while you fry the eggs in the same pan and toast the bread. This would be a good time to reheat the sauce if need be.
Butter the toast, scrape over a little more mustard and place the burgers on their platforms. Spoon over the onion gravy, crown with the eggs, sprinkle over the chives and season with a scratch of sea salt and black pepper.