Prepare the Pesto: In a food processor, combine basil, garlic, walnuts, and Parmesan cheese. Season with salt and pepper. Pulse until combined.
With the food processor running, slowly pour in the olive oil until the mixture is smooth and emulsified.
Assemble: Spread the fresh pesto equally on all 4 slices of sourdough bread.
Pre Toast: Place two slices of bread (pesto side up) on the panini maker or in a toaster oven for about 2 minutes to warm the bread.
Layer: Place the mozzarella cheese slices, tomato slices, and roasted red peppers on top of the two warmed bread slices.
Keep the panini maker open and allow the cheese to start melting and the vegetables to soften.
Press: Once the cheese begins to melt, place the remaining two slices of bread on top to close the sandwiches.
Close the panini maker lid and press for 2 to 3 minutes until the bread is golden brown and crispy.
Remove carefully, slice in half, and serve immediately.