Put the flour in a bowl, add the butter to the flour and rub in with your fingertips until it resembles breadcrumbs. Add the grated cheddar into the pastry and mix. Add 3 tbsp cold water and mix until the pastry forms a ball. Wrap in cling film and chill for 5 mins. Butter a 20 x 6cm deep loose-bottom tart tin, or a 35 x 12cm rectangular tart tin.
Heat oven to 180C/fan 160C/gas 4. Lightly dust the work surface with flour, roll out the pastry and line the tin. Chill in the freezer for 20 mins, then line the pastry case with baking paper, fill with beans and cook for 15 mins. Remove the beans and paper, then return the pastry case to the oven for 10 mins.
Crack the eggs into a jug, whisk, then add the milk and whisk again. Sprinkle half the grated cheese over the pastry case, then add the asparagus, egg mix and remaining cheese (if using a rectangular tin, you may not need all the mixture, so add it gradually). Bake in the lower half of the oven for 30-35 mins or until the egg mix is set.