Place all pico de gallo ingredients (but only half the lime juice) into a small bowl and toss together.
In a large pot, melt butter over medium heat.
Add ⅓ of the pico and saute for 2 to 3 minutes. Season with salt and pepper.
Add flour and stir together until no dry lumps remain and the flour no longer has a ‘raw’ taste, 3 to 4 minutes.
Whisk milk than stock into the mixture, until full combined and continue to stir until mixture thickens enough to barely coat the back of a spoon.
Combine cheeses together in a bowl and toss together with remaining lime juice.
Remove pot from heat and slowly stir in cheese, in small handfuls until all cheese has been added and soup is smooth. Stir in paprika and chile powder and season with salt and pepper.
Fold in beans, half the corn and remaining pico until fully incorporated and simmer for 6 to 8 minutes, stirring occasionally. Adjust seasonings as needed.
Ladle chowder into bowls and top with a huge handful of corn chips, the remaining corn, crumbled cheese, cilantro leaves, hot sauce, and sliced serranos (if using). Serve.