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Step 1
For pasta dough, place flour on a work surface. Make a well in the centre and add eggs, egg yolks, oil and 1 tsp salt flakes. Combine and knead to a smooth dough (8-10 minutes; alternatively, process in a mixer fitted with the dough hook attachment.) Cover and set aside to rest for 20 minutes.
Step 2
Divide dough into 4 pieces. Working with one piece at a time (cover remaining dough with plastic wrap to stop it drying out), roll through a pasta machine, starting at the widest setting, then reducing settings notch by notch until pasta is 2.5-3mm thick. Set sheets aside on a lightly floured tray for 10 minutes, then cut into 3cm-wide pieces. Hang and dry pasta until required.
Step 3
Heat oil and butter in a wide saucepan over low heat. Add vegetables, garlic and chilli and cook, stirring occasionally, until vegetables are tender but not browned (6-8 minutes). Increase heat to medium, add meat and cook, stirring continuously, until liquid evaporates (6-8 minutes). Add wine and Madeira and cook, stirring occasionally, until alcohol evaporates (4 minutes). Season to taste and add tomato passata, basil and 250ml water. Bring to a simmer, reduce heat to low and cook, stirring occasionally, until meat is tender (1 hour).
Step 4
Add pasta to a large saucepan of boiling salted water and cook until al dente (2-3 minutes). Remove with tongs or drain in a sieve, then add to ragù and toss to combine. Serve topped with fresh finely grated parmesan.