In a small bowl combine 2 tablespoons of vegan mayo and the pesto. Set aside.
In another bowl combine the remaining vegan mayo, vegan feta and dijon mustard. Set aside.
Spread butter on one side of each piece of bread. Turn over one slice and layer the feta, roasted peppers and basil. Turn over the other slice and spread on some vegan pesto and top with spinach. Close the sandwich and repeat with the other sandwich ingredients.
Heat a skillet over medium heat. Add the sandwiches and cook until browned on both sides (approx. 2-3 minutes per side).