Combine softened cream cheese, chopped pepperoncini peppers, and a splash of pepperoncini juice in a medium mixing bowl. Add garlic powder and dried oregano, then season with salt and pepper. Mix until smooth.

Transfer to a serving container, cover with plastic wrap, and refrigerate for at least 15 minutes.

Preheat oven to 350°F (175°C). Slice bagels in half and cut into wedges. Toss bagel wedges with olive oil, garlic powder, and kosher salt.

Spread bagel pieces on a lined baking sheet and bake for about 15 minutes, flipping halfway through until golden brown.

Serve the chilled dip alongside crispy bagel chips or with fresh vegetable sticks.