In the bowl of a stand mixer fitted with the paddle attachment, combine 1 cup (127g) flour, 2 tablespoons (4g) basil, yeast, kosher salt, garlic powder, 1 teaspoon thyme, 1 teaspoon oregano, and 1 teaspoon rosemary until well combined.
In a medium saucepan, combine 1/2 cup (120g) milk and 6 tablespoons (84g) butter; cook over medium heat until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add milk mixture to flour mixture; beat at medium speed for 2 minutes. Add potatoes, honey, and 1 egg (50g); beat at medium-high speed for 2 minutes. With mixer on medium-low speed, gradually add 2 cups (254g) flour, beating just until combined.
Switch to the dough hook attachment; beat at medium-low speed for 4 to 6 minutes, adding up to remaining 1/4 cup (32g) flour, 1 tablespoon (8g) at a time, until a smooth, elastic dough forms. (Dough should pass the windowpane test [see Note]; scrape sides of bowl and dough hook as needed.)
Spray a large bowl with cooking spray; place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 40 minutes to 1 hour.
Line a rimmed baking sheet with parchment paper. Cut cheese into 0.25-ounce (7g) cubes.
Punch down dough. Turn out dough, and divide into 23 portions (about 35g); cover with a piece of plastic wrap. (You should not need much additional flour, if any.) Flatten 1 piece of dough, and place 1 cheese cube in center; pinch dough closed, and gently shape into a ball, pressing together any seams, if needed. Repeat with remaining dough. Place balls, seam side down, on prepared pan in a Christmas tree shape, starting with 2 balls for the trunk and 6 balls for the first row; reduce each following row by 1 ball, leaving a ¼-inch gap between each. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 40 minutes to 1 hour.
Preheat oven to 375°F (190°C).
In a small bowl, whisk together remaining 1 egg (50g) and remaining 1 tablespoon (15g) milk; brush onto rolls.
Bake until golden brown and an instant-read thermometer inserted in the center registers 190°F (88°C), 15 to 20 minutes.
Make marinara sauce: In a small saucepan, heat oil over medium heat. Add garlic and tomato paste; cook, stirring frequently, for 2 minutes. Add tomatoes, and bring to a boil. Reduce heat to medium-low; simmer for 10 minutes. Stir in basil, honey, salt, and pepper.
In a small bowl, stir together remaining 4 tablespoons (56g) butter, remaining 1 tablespoon (2g) basil, remaining 1 teaspoon thyme, remaining 1 teaspoon oregano, and remaining 1 teaspoon rosemary. Brush herb butter onto rolls. Serve warm with Marinara Sauce. Garnish with sea salt and crushed red pepper, if desired.