Step 1 For the Goat Cheese Filling:
Combine the goat cheese and cream in a medium bowl and beat together using an electric mixer (or stand mixer) until light and fluffy. Season with salt and pepper.
Step 2 For the Herb Oil:
Combine the herbs in a food processor and pulse a few times to chop them. With the machine running, add the oil in a slow stream and process until very smooth with visible flecks of the herbs remaining. Season with salt and pepper. Transfer the oil to a small bowl (or jar), cover, and set aside.
Step 3 Toast the Walnuts:
Toast the walnuts in a small, dry skillet over medium heat until they begin to darken slightly and are fragrant. Transfer the nuts to a cutting board to cool slightly, then chop them coarsely.
Step 4 Plating the Dish:
Place one tomato slice on each plate. Top each slice with a spoonful of the goat cheese mixture. Top each plate with another tomato slice and another spoonful of the goat cheese filling. Drizzle each strata with some of the herb oil, and sprinkle with the walnuts.