Make the sun-dried tomato pesto by combining walnuts, sun-dried tomatoes, olive oil, parmesan, basil, lemon, salt, pepper and garlic in a food processor. Pulse until combined. Season to taste.
Combine softened goat cheese, basil and a drizzle of olive oil together. Scoop pesto onto sourdough bread and spread in an even layer. Top with shredded mozzarella cheese and goat cheese.
Add oil to a skillet and add sandwich. Cook for about 4-5 min per side on medium to low heat, until cheese is melty and the bread is golden brown. Enjoy!