Preheat oven to 400°F (200°C).

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

In a medium bowl, stir together buttermilk and tomatoes. Make a well in center of mixture.

Add buttermilk mixture to dry ingredients. With one hand holding bowl, use other hand to slowly fold flour mixture from sides of bowl into buttermilk mixture until dough is soft but not too wet.

Turn out dough onto a lightly floured surface. Using your hands, 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 a 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). Add shallots, and fry in batches, if necessary, stirring frequently, until deep golden brown and crispy, 8 to 10 minutes, reducing heat if they brown too quickly. 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.