Using a fine grater, grate white onion over a bowl fitted with a fine mesh strainer to collect the juice. Discard the solids.
In a pitcher, combine together the freshly squeezed onion juice with the rest of the ingredients except the garnish. Stir well until all salt is fully dissolved. Adjust the seasonings to taste if needed. Transfer a pitcher to a refrigerator and chill Sangrita overnight or longer.
Serve ice cold Sangrita Valentina in shot glasses garnished with a small amount of fresh Pico de Gallo along with shot glasses filled with tequila. The best tequila choice to accompany Sangrita Valentina is Arrogante Blanco or Arrogante Reposado. Drink a shot of tequila first and follow up with a Sangrita chaser.