In a food processor, blend the bread, 1/2 cup softened butter and 3 tablespoons grated Parmesan cheese. Spray cooking oil in the bottom of a nonstick 91/2-inch springform pan. Cut a piece of parchment to fit the bottom of the pan. Press crumb mixture into pan, going up 1/4 inch on sides. Refrigerate.
Beat the cream cheese until smooth in a sturdy electric mixer. Add chopped onion, 1/4 cup grated Parmesan cheese, 1/4 cup melted and cooled butter, 1 tablespoon oil and herbs from the tomato jar, and the basil. Add eggs, 7 tablespoons chopped sun-dried tomatoes and sour cream, blending until smooth.
Pour a third of the filling into the refrigerated crust. Add a layer of about 15 coarsely chopped sun-dried tomatoes, followed by another third of the filling. Add a thin layer of pesto (don’t go too close to the edge with this) and remaining third of filling.
Bake 50-60 minutes on second-to-lowest rack of oven, placing a foil sheet underneath to catch drippings. When set in center, turn off oven and let the cheesecake sit 20 more minutes. Cool and refrigerate for a day.
Remove sides of pan and place cheesecake on a serving platter. Garnish with fresh basil leaves and pieces of sundried tomato. Enjoy with crackers or rustic breads.