Warm 3 tablespoons butter in a large skillet over medium heat. Add sliced bread and toast until golden brown, flipping occasionally (about 3 minutes). Take the bread from the skillet and add the walnuts with additional 1 tablespoon of butter. Once the butter has melted, stir the walnuts to coat. Cook until lightly brown and fragrant (about 3 minutes), stirring occasionally. Set walnuts aside to cool.

In a food processor, combine cooled walnuts, ricotta cheese, 1 tablespoon lemon juice, 1/4 teaspoon kosher salt and 1/2 teaspoon freshly ground black pepper. Pulse until just smooth. Season to taste with additional kosher salt (you may need about 1/4 teaspoon more if your ricotta is unsalted).

Place eggs in a small saucepan and cover with lukewarm water. Place the saucepan over high heat and bring the water to a boil. As soon as the water starts to boil, turn the heat off and cover the saucepan. Let sit for 1 minute then transfer to the sink. Run cold water over the eggs while tipping the pan to let the hot water drain for about 30 seconds. Peel eggs under cold, running water.

Toss arugula with remaining 1 tablespoon lemon juice and a small pinch of kosher salt.

To serve, spread walnut-ricotta mixture on the whole wheat crostini. Divide arugula amongst the slices. Place a soft-boiled egg on each slice then gently cut in half to break the yolk. Finish each crostini with a very light drizzle of extra-virgin olive oil, black pepper and a few flakes of sea salt.