Preheat oven to 400°F (200°C).

In a large bowl, whisk together flour, baking soda, kosher salt, paprika, and red pepper until combined. Make a well in center.

In a medium bowl, stir together buttermilk and tomatoes. Add buttermilk mixture to flour mixture. Using one hand like a claw, slowly fold flour mixture from sides of bowl into buttermilk mixture until dough is soft but not too wet.

Line a baking sheet with parchment paper.

Turn out dough onto a lightly floured surface, and shape into an 8-inch square (1-inch thickness). Sprinkle with cheese. Using a sharp knife, cut into 9 squares, and place 1 inch apart on prepared baking sheet.

Bake until golden brown, about 18 minutes. Remove from pan, and let cool on a wire rack.

In a 10-inch cast-iron skillet, pour oil to a depth of ½ inch, and heat over medium heat until an instant-read thermometer registers 350°F (180°C).

Fry shallots, in batches if necessary, stirring frequently, until deep golden brown and crispy, 8 to 10 minutes, adjusting heat as needed. Remove shallots using tongs, and let drain on a paper towel-lined plate for 5 minutes.

In the work bowl of a food processor, place shallots, butter, and sea salt; pulse just until combined, and transfer to a small bowl. Serve at room temperature with warm rolls.