Heat olive oil over medium heat in a large fry pan or 5 qt Dutch oven.
Add the onion, celery and carrot and saute 10 minutes, or until onion starts to soften. Stir in the garlic.
Add the ground beef/beef mince and break up into small chunks. Cook for 5 minutes until the beef starts to brown.
Add the tomato paste and stir through.
Deglaze the pan with the red wine. To deglaze, pour in the red wine and use your spoon to gently scrape at the bottom of your pan to release the flavours.
Add the beef stock and tin tomatoes. Bring to the boil, and reduce heat to simmer for 40 minutes covered.
Remove lid, and simmer for a further 30 minutes. The sauce should be thickened without being too dry or watery. You should see a small amount of liquid on top of the meat sauce.
White Sauce
Melt butter in a small saucepan on a medium heat.
Add flour and stir to form a doughy consistency. Add the seeded mustard, and fry the dough for two minutes.
Very slowly, add the milk and use a whisk to gently whisk out the lumps.
Continue to whisk the roux for 10-15 minutes, until the sauce starts to thicken. There should be no lumps visible and the sauce should get nice and thick. Use a whisk to reduce lumps.
Add the cheese and whisk a further 2 minutes until the cheese has melted.
Assembly
Preheat oven to 350F/180C.
In your dish, assemble the lasagne in the following order - meat, pasta and sauce.
Make sure you finish with a white cheese sauce layer. Optional - sprinkle with a little more cheese.
Cook in the oven for 45-60 minutes until the lasagne is browned on top and the pasta is cooked through. If you find it browning too much or burning, cover the lasagne with tin foil.
Notes
Note - 'prep time' for this recipe includes the cooking time for the meat and white sauce, 'cooking time' is the time taken to actually bake the lasagne!