Warm the oil and butter in a medium saucepan over medium-high heat. Add the onion and rice and cook, stirring frequently, for 1 to 3 minutes, until edges of rice turn slightly translucent and liquid is absorbed. Stir in salt, black pepper to taste, ground red pepper, and 4 cups of water. Bring to a boil, reduce heat to low, cover, and simmer without stirring for about 15 minutes, until rice is al dente and most liquid is absorbed (the mixture will be creamy). Remove from heat and stir in the Parmesan and Cheddar cheeses. Taste and add additional salt and pepper if needed. Set aside until cool enough to handle comfortably, about 45 minutes.
To make the balls, moisten hands with water. Form about 2 heaping tablespoons of cooked rice into a ball, then press 1 piece of Gouda into the center. Reshape so that rice completely encloses the cheese and squeeze to make a compact ball. Set aside and repeat with remaining rice. Roll the balls in the panko crumbs.
Heat oil in a heavy-bottomed, deep-sided pan (such as a Dutch oven) to 355 to 360 degrees. Working in batches of 5 balls at a time so as not to crowd the pan, gently lower the balls into the oil and fry, turning once or twice, until deep golden brown, 3 to 4 minutes. Drain on paper towels and serve hot. Repeat with remaining balls, allowing the oil to return to 360 degrees before adding a new batch.