Combine egg yolks, vinegar, mustard, sugar, salt, and pepper in a small food processor.
Pulse until combined, then gradually pour in 150ml of oil while blending until thick.
Add shallot, garlic, capers, herbs, and lemon juice then blend until finely chopped.
Add 15ml of cold water and blend briefly until the sauce reach a spoonable consistency.
Divide the sauce into four ramekins and set aside.
Cut herring fillets in half lengthways and remove any pin-bones from the flesh.
Slice each fillet into diagonal pieces, rinse under cold water, and drain well.
Heat 750ml of oil in a saucepan to 180°C.
Mix flour, semolina, mustard powder, cayenne, salt, and pepper in a large bowl.
Dredge damp fish pieces in the seasoned flour and shake off any excess.
Fry fish in batches for 3 minutes until golden-brown and crisp.
Drain fried fish on kitchen paper and serve hot with the green sauce and lemon wedges.