Poach eight eggs. To poach eggs, fill a saucepan with about 3 inches (8 cm) of water and add a splash of vinegar. Heat the water until it gently simmers then break a cold egg into a small dish. Holding the dish just above the simmering water, gently slip the egg into the water.
Repeat this step for remaining eggs. Cook the eggs in the simmering water until whites are set and yolks are cooked as desired, 3 to 5 minutes. Remove the eggs with a slotted spoon and place them on a paper towel to drain.
Lay the eight strips of bacon on a baking tray lined with non-stick aluminum foil or parchment paper. Roast in the same 425°F (218°C) oven as used for the tomatoes (see below) until golden and crispy about 6-7 minutes.
Slice the brioche into 1¼ inch (3 cm) thick pieces. Using a 3½ or 4-inch (10 cm) cookie cutter or ring mold, cut out rounds from the bread. This can also be done by trimming away the side crusts of the bread with a serrated knife.
Lightly butter each side of the bread rounds and pan-fry over medium-high heat in a non-stick skillet. When well browned and crispy on both sides, remove and set aside before assembly.
Preheat oven to 425°F (218°C). Cut the tomatoes in half through the middle and lay the halves in a single layer on a baking tray lined with non-stick aluminum foil. Make sure the cut halves are facing upwards.
In a small bowl, mix the sugar, sea salt, black pepper, and dried basil. Sprinkle this dry mixture evenly over the tomato halves. Drizzle the red wine vinegar and olive oil over the tomatoes then add the grated parmesan cheese (optional).
Bake in the oven for 12-15 minutes until the tomatoes are slightly collapsed and have a lovely, slightly caramelized appearance. Depending on the actual size and ripeness, you may have to lengthen or shorten the roasting times by a few minutes. If using larger tomatoes, you can roast these for up to 30 minutes.
Place the egg yolks, water, and lemon juice in a bowl and whisk very well until slightly lightened in colour (about 90 seconds).
Place the bowl over a pan of gently simmering water and whisk continuously until the eggs begin to thicken. Watch them closely and remove from the heat if they seem to be cooking too quickly. When the whisk leaves a clean line in the eggs, they are ready.
Off the heat, begin whisking in the very soft butter a tablespoon or so at a time. Whisking continuously, add more butter once the butter in the pan has emulsified into the eggs. When half the butter is gone and the sauce is looking smooth, you can increase the amount of butter you add. When the sauce is thick and has the consistency of mayonnaise, it is ready. Season with salt.
Remove the chipotle peppers and adobo sauce from the can and purée into a paste using either a handheld stick blender or a food processor. When smooth, add chipotle paste to the base hollandaise sauce. Set the finished hollandaise aside for assembly of the dish.
Warm four plates in the oven and place two rounds of brioche on each plate. Place several leaves of arugula on the bread, followed by a single, long piece of bacon. Place two halves of roasted tomatoes on each piece of bread, cut side up.
Carefully place a poached egg that has been reheated in the fresh water for 90 seconds on each portion, as per directions above. Place a heaping tablespoon of hollandaise sauce over each warm egg and garnish with a sprinkling of freshly cut chives. Serve immediately.