Line a large baking sheet with parchment paper and set aside. Stir together panko and ⅓ cup cream in a large bowl; let sit until absorbed, about 10 minutes. Add egg and beat lightly into breadcrumbs with a fork. Add ricotta, 1 cup Parmigiano-Reggiano, ½ teaspoon garlic, 2 teaspoons Italian seasoning, and 1 ½ teaspoons salt; stir to combine. Add chicken and mix gently with a fork until incorporated (do not overmix). Cover and refrigerate until chilled and easy to handle; about 30 minutes. (If the mixture is still too soft to handle, chill for an additional 10 minutes before shaping.) Roll meatballs into about 30 (1 ½-inch) balls (about 1 ½ ounces each) and place on prepared baking sheet.

Heat 2 tablespoons reserved sun-dried tomato oil in a large nonstick skillet over medium. Working in two batches and keeping remaining meatballs chilled, add half the meatballs to skillet and cook, turning occasionally and adjusting heat as needed, until browned on all sides, and an instant-read thermometer registers 165°F, 8 to 13 minutes. Transfer meatballs to a shallow bowl and cover tightly with aluminum foil to keep warm. Wipe skillet clean, if needed. Repeat with remaining 2 tablespoons reserved sun-dried tomato oil and meatballs. Do not wipe skillet clean.

To remaining oil in skillet, add shallot; cook, over medium, stirring occasionally, until softened, about 1 minute. Add red pepper, remaining 1 teaspoon garlic, and remaining ½ teaspoon salt; cook, stirring constantly, until fragrant, about 30 seconds. Add tomato paste, sun-dried tomatoes, and remaining 1 teaspoon Italian seasoning; cook, stirring constantly, until tomato paste has darkened in color, about 1 minute. Pour chicken stock and remaining ¼ cup cream into skillet; cook, stirring occasionally, until sauce is slightly reduced, about 3 to 4 minutes. Stirring constantly, gradually add remaining ½ cup Parmigiano-Reggiano, until sauce is smooth and slightly thickened, about 1 minute. Return meatballs to skillet, turning to coat in sauce. Garnish with parsley.