Beat 2 (8-ounce) packages cream cheese, butter, 1/2 teaspoon salt, and pepper at medium speed with an electric mixer until creamy. Set aside.
Process dried tomatoes in a food processor until chopped.
Add 1 (3-ounce) package cream cheese, tomato paste, and 1/4 teaspoon salt; process until smooth, stopping to scrape down sides. Spoon into a bowl, and set aside. Wipe container of food processor clean.
Process garlic and next 4 ingredients in food processor until chopped.
Add Parmesan cheese, remaining 3-ounce package cream cheese, and remaining 1/4 teaspoon salt; pulse just until blended, stopping to scrape down sides.
Spray a 6-inch springform pan with cooking spray.
Spread 1/2 cup butter mixture evenly on bottom of springform pan.
Layer with half of tomato mixture, 1/2 cup butter mixture, and half of basil mixture; top with 1/2 cup butter mixture. Repeat layers with remaining tomato mixture, 1/2 cup butter mixture, and remaining basil mixture. Top with remaining butter mixture. Cover with plastic wrap; chill at least 8 hours.
Run a knife gently around edge of pan to loosen sides.
Remove sides of pan; carefully remove bottom of pan, and place layered spread on a serving tray.