Prepare the Smoked Tomato Sauce:

1. Prepare smoker according to manufacturer's instructions, bringing internal temperature to 250°F to 275°F; maintain temperature 15 to 20 minutes. Place tomatoes in a medium-size stainless-steel skillet. Smoke tomatoes, maintaining temperature inside smoker between 250°F and 275°F, until tomatoes are perfumed with smoky flavor, about 30 minutes.

2. Transfer smoked tomatoes, along with any juices, to a blender. Process until smooth, about 20 seconds. Pour into a small saucepan; bring to a simmer over medium-low. Simmer, stirring occasionally, until slightly thickened, about 10 minutes. Remove from heat.

3. While tomato sauce simmers, heat oil in a medium skillet over medium-high. Add andouille; cook, stirring occasionally, until crisp and browned, about 2 minutes. Remove from heat.

4. Transfer tomato sauce and browned andouille, along with any drippings in skillet, to a blender. Process until smooth, about 25 seconds. Set a fine mesh strainer over a medium saucepan. Using a rubber spatula, push tomato mixture through strainer into saucepan; discard solids. Stir salt into strained tomato puree. Cover until ready to serve.

Prepare the Shrimp-And-Grits Balls:

1. Bring water to a boil in a small saucepan over medium-high. Add salt. Gradually whisk in grits until smooth and no lumps remain. Reduce heat to medium. Add butter, and whisk constantly until melted, about 1 minute. Reduce heat to low; cook, whisking occasionally, until grits are thickened and tender to the bite, about 5 minutes. Remove from heat. Spread grits on a 9- x 13-inch rimmed baking sheet. Let cool to room temperature, about 20 minutes.

2. Meanwhile, toss together shrimp and Creole seasoning in a medium bowl. Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high. Add shrimp; cook until opaque throughout and pink, about 2 minutes per side. Transfer cooked shrimp to a work surface; let cool 5 minutes. Coarsely chop shrimp, and set aside. Wipe skillet clean.

3. Add remaining 1 tablespoon oil to cleaned skillet; heat over medium. Add jalapeños and garlic; cook, stirring often, until fragrant, about 30 seconds. Remove from heat. Scrape mixture into a small bowl.

4. Transfer grits to a large bowl, and break apart into small clumps. Add jalapeño mixture, mild cheddar cheese, white cheddar cheese, parsley, dill, basil, and tarragon; stir until thoroughly blended. Add chopped shrimp, and stir until combined.

5. Line a large rimmed baking sheet with parchment paper. Using a 1-ounce (2-tablespoon) scoop, scoop 1 portion shrimp mixture into your hands, and roll into a ball (you'll have 24 balls total). Place on prepared baking sheet. Repeat process with remaining shrimp mixture. Chill, uncovered, until cold and firm, about 30 minutes.

6. Meanwhile, pour oil to a depth of 2 inches into a medium-size Dutch oven; heat over medium until oil reaches 350°F. Whisk together egg, milk, and buttermilk in a shallow bowl. Place panko and flour in 2 separate shallow bowls.

7. Working with 1 Shrimp-And-Grits Ball at a time, dredge balls in flour, and shake off excess. Roll ball in egg mixture; let excess drip off. Roll in panko to coat, pressing to adhere. Return to baking sheet.

8. Working in 4 batches, fry Shrimp-And-Grits Balls, turning occasionally using a slotted spoon or spider, until golden brown, about 3 minutes per batch. Transfer to a baking sheet lined with paper towels to drain.

9. Uncover Smoked Tomato Sauce in pan, and place over medium heat. Cook, stirring often, until hot, about 3 minutes. Remove from heat. Ladle 1/4 cup Smoked Tomato Sauce into each of 6 shallow bowls. Top each with 4 Shrimp-And-Grits Balls. Garnish with Pecorino Romano and baby greens.