In a wide sauce pan, bring a few inches of water, plus the vinegar, to a simmer.
In a bowl, whip together the softened goat cheese, sour cream, thyme, basil, garlic powder, and salt and black pepper to taste (You can use an electric handheld mixer or just a spatula, like I do).
Working with batches of 2-3 eggs at a time, crack each egg into individual bowls. Drop them one at a time into the simmering water. Poach the eggs for about 4-5 minutes per batch for runny yolks.
When finished poaching, lift the eggs with a slotted spoon and place onto a plate lined with paper towels to drain slightly before plating.
While the eggs poach, slice and toast the bread, and slice the avocado.
To plate, swipe 2-3 tablespoons of the herbed goat cheese onto a plate. Place two poached eggs onto the goat cheese and sprinkle with paprika. Add ½ cup baby arugula to the plate and top with a few slices of avocado.
Sprinkle all over with salt, freshly ground black pepper, and freshly squeezed lemon juice.
Serve with the crusty toast.