Mound flour on a clean surface and create a well. Add eggs, olive oil, and salt into the well. Using a fork, gradually incorporate flour into the eggs until a shaggy dough forms. Knead by hand for 8-10 minutes until smooth and elastic. Wrap in plastic and rest at room temperature for 30 minutes.
In a heavy pot, heat olive oil over medium-high. Brown beef and pork in batches. Remove meat. Reduce heat to medium, add onion, carrot, celery, and garlic; sauté until softened. Deglaze with red wine, scraping up bits. Return meat, add broth and bay leaf. Bring to a simmer, cover, and cook on low for 1.5 hours or until meat is fork-tender. Discard bay leaf and let cool.
Wilt spinach in a pan with a splash of water, drain thoroughly, and squeeze out excess moisture. Finely chop. In a food processor, pulse cooled meat mixture (with vegetables) until coarsely ground. Combine chopped spinach, ground meat, Parmigiano-Reggiano, egg yolk, nutmeg, salt, and pepper. Mix until cohesive. Transfer to a piping bag or ziplock bag.
Divide rested dough into 4 pieces. Keep covered. Flatten one piece, then pass through a pasta roller on the widest setting, folding and re-rolling until smooth. Gradually roll to the second-thinnest setting (about 1 mm thick). Lay the sheet on a lightly floured surface.
Pipe small dots of filling (about 1 tsp) in a line along the lower third of the pasta sheet, leaving 1 inch between each. Fold the top edge down over the filling. Press around each mound to seal, then use a fluted pastry wheel to cut between the mounds, creating small pillows. Pinch each sealed edge firmly (the 'plin') to ensure closure.
Bring a large pot of generously salted water to a gentle boil. Drop in agnolotti in batches and cook for 3-4 minutes or until they float to the surface. Reserve 1/4 cup pasta water, then drain.
In a large skillet, melt butter over medium heat. Add sage leaves and cook until butter is golden and nutty and sage is crisp, about 2-3 minutes. Remove from heat. Add drained agnolotti and a splash of reserved pasta water, tossing gently to coat. Season with salt.
Divide agnolotti among warm bowls. Spoon any remaining sage butter over top. Finish with shaved Parmigiano-Reggiano and cracked black pepper. Serve immediately.