In a bowl, whisk beer into flour until smooth and stir in salt. Make several shallow cuts across inside curve of each shrimp and press shrimp gently (to help prevent curling during cooking).
In a 3-quart saucepan heat 2 inches oil to 375°F. Working in batches of 4 or 5 pieces, dredge shrimps in batter to coat completely, letting excess drip off, and fry, turning, until golden, about 3 minutes. Transfer tempura as fried to brown paper with tongs to drain and season with salt and gently sprinkle matcha powder over fried shrimps.
Serve shrimp tempura with soy sauce and daikon oroshi.