Preheat the broiler on high and place the oven rack 4 to 5” below the broiler.
Slice the pepper into slabs. Brush each side with olive oil.
Place garlic cloves and shallots into the center of a foil packet and drizzle with remaining olive oil. Add a pinch of red pepper flakes and close foil into a ball. Place under the broiler.
Line a baking sheet with foil and spray lightly with nonstick cooking spray. Arrange peppers on the foil. Add peppers to the oven and broil for 4 minutes.
Turn the peppers over. Broil for 3 more minutes.
Remove peppers, garlic, and shallots from the oven.
Add peppers, garlic, and shallots to a bowl and cover. Let steam for 10 minutes.
*This step will further soften the peppers. You may skip this step if you prefer peeling the peppers for a smoother dip, but I find the roasted/slightly charred skin gives a delicious smoky flavor and perfect texture to this dip. I highly suggest trying it this way!
Meanwhile, heat a frying pan over medium high heat.
Next, add the peppers, garlic, and shallots to a food processor along with basil and parmesan. Purée.
Add olive oil to the pan and swirl to coat. Add the puréed vegetables. Sauté for 2 minutes, then add the tomato paste. Stir and cook for 3 minutes.
Remove from heat and add back to the food processor. Purée for 10 to 15 seconds.
In a medium mixing bowl, combine this with the softened cream cheese, salt, and pepper. Mix thoroughly.
Garnish with a pinch of red pepper flakes and basil leaves. Serve with pita chips or crackers