In a large mixing bowl, combine the softened cream cheese, shredded cheddar, chopped parsley, and chives. Mix with a fork or spatula until smooth and evenly blended, with a creamy, uniform texture.
Add smoked paprika, cayenne pepper, a pinch of salt, and pepper to the cheese mixture. Stir thoroughly to distribute the spices evenly, filling the air with an inviting aroma of smoky herbs.
Scoop about 1 tablespoon of the cheese mixture and gently roll it between your palms to form a small, smooth sphere. Place the shaped cheese ball on a parchment-lined baking sheet. Repeat until all the mixture is used, aiming for 12-15 evenly sized balls.
Place the breadcrumbs in a small bowl. Roll each cheese ball gently in the breadcrumbs, pressing lightly to ensure an even coating. This step creates a crispy crust once fried.
Pour vegetable oil into a deep frying pan or pot, enough to submerge the cheese balls. Heat the oil over medium-high heat until it reaches approximately 180°C (350°F), or until a small piece of bread sizzles and turns golden within seconds.
Carefully lower the cheese balls into the hot oil in batches, making sure not to overcrowd the pan. Fry for about 2-3 minutes, turning gently with a slotted spoon, until the exterior is golden brown and crispy, and the cheese inside is warm and melty.
Using a slotted spoon, transfer the fried cheese balls onto paper towels to drain excess oil. Let them rest for about 2 minutes to set and avoid burning your palate.
Arrange the cheese balls on a serving platter. Serve warm, garnished with extra chopped herbs if desired, and enjoy their crispy exterior and gooey interior in every bite.