Cut the baguette in half, and then divide the halved baguette into four equal-sized pieces.
Toast the bread lightly until it is just beginning to take on some color, but is still soft.
Remove the toasted baguette pieces from the toaster.
Spread the 4 Tbsp of softened butter over the toasted baguette slices, and set the toasted bread aside.
Whisk the whole eggs in a large bowl until they arrive at a uniform consistency.
Add 2 Tbsp of salted butter to a sauté pan over medium-low heat, and add the eight eggs that you whisked earlier.
Season the eggs with a small pinch (roughly ¼ tsp) of Kosher salt, and stir with a rubber spatula once you see the egg beginning to cook on the bottom of the pan.
Reduce the heat to low, and continue to cook until the eggs are almost fully cooked, but still very soft and slightly runny.
*This should take about 6 minutes when cooking over low or medium-low heat.
Remove the eggs from the stove, and set aside.
Top each piece of toasted baguette with the scrambled eggs that you cooked earlier.
Top the scrambled eggs with a few pieces of thinly-sliced smoked salmon
Top each piece of bread with a scoop of the salmon roe, some crème fraiche, some sliced chives, and some chopped dill.
Drizzle a bit of extra virgin olive oil over each assembled piece of toast, and serve immediately.