To make the dough: Place whole potatoes in a large pot, add enough cold water to cover and bring to a boil. It is important to keep potatoes whole while boiling so that they conserve the level of starchiness necessary for shaping of rellenos. Add 1/4 cup of salt to boiling water and cook for about 45 minutes until potatoes are fork-tender.
Drain potatoes and while still hot, break potatoes down with a masher or wire whisk until free of large lumps, but not completely smooth. Season mashed potatoes with 1 teaspoon of salt, and set aside to cool until they are easier to handle with your hands.
For the Picadillo: In a large sauté pan over medium-high heat, warm olive oil. Add onion, and cook for about 2 minutes until it loses its raw taste. Add red pepper, garlic, and sofrito, and cook, stirring, for another 3 minutes. Stir in tomato sauce, cilantro and oregano, season with 2 tablespoons of salt, and cook for another minute.
Add meat and cook for about 4 minutes, stirring and breaking up the beef as it cooks. Season with another tablespoon of salt and continue to cook for 20 minutes, stirring occasionally until meat is cooked through, liquid has evaporated and flavors have concentrated.
To make rellenos: Dip an ice cream scoop in water and tightly pack it with mashed potatoes. Dip your forefinger in olive oil and press into center of potatoes to make a cavity, without reaching all the way through. Rotate your finger inside to widen cavity. Stuff cavity with 1 teaspoon of picadillo and 1/2 teaspoon of cream cheese and press down gently.
Empty stuffed dumpling into your hand and carefully seal cavity by folding mashed potatoes over it. (Make sure that it is evenly sealed to ensure that no stuffing leaks out when frying rellenos). Gently roll dumpling into a smooth ball. Repeat with remaining mashed potatoes, meat and cheese. (Remember to dip ice cream scoop in water before packing it with mashed potatoes, so that dumplings release themselves easily).
In a frying pan, heat about 3 inches of vegetable oil to 350°F. Dredge rellenos de papa in cornstarch, patting off any excess. Using a slotted spoon, carefully lower them into hot oil. Fry for 3 to 4 minutes, turning occasionally if necessary, until golden.
Using a slotted spoon, remove rellenos from oil, and set aside to drain on paper towels. Serve immediately.