Crusty onion and cheese muffins

Ingredients

• 1/4 cup (35 grams) plain flour
• 20 gram butter
• 1 teaspoon water, approximately
• 1 tablespoon vegetable oil
• 1 medium onion, halved, sliced
• 1 3/4 cup (260 grams) self-raising flour
• 3/4 cup (110 grams) plain flour, extra
• 3/4 cup (90 grams) grated tasty cheddar cheese
• 1 tablespoon chopped fresh chives
• 1 egg, lightly beaten
• 1 1/4 cup (310 millilitres) buttermilk
• 1/2 cup (125 millilitres) vegetable oil, extra
• 40 gram packaged cream cheese, softened
• Chive butter
• 50 gram butter, softened
• 2 teaspoon lemon juice