To prepare the pasta, mix the flours with salt in a big bowl, make a hole in the middle, add the beaten egg and water, whisk to combine and knead for 10 minutes to obtain an elastic dough. Set aside to rest for 30 minutes.
Put the pesto ingredients in a food processor and pulse to obtain a creamy mixture. Transfer in a serving jar.
Wash the tomatoes with plenty of water, drain well and cut in quarters.
Heat the oil over medium heat in a cast-iron skillet, add the crushed garlic and fry for 30 seconds, just to flavor the oil.
Add the tomatoes, wine and freshly ground black pepper, stir to combine, cover the skillet with a lid and let simmer for 5-7 minutes over low heat, until the liquid starts to thicken. Remove from the heat.
Roll the pasta dough as thin as possible with a rolling pin on a well-floured surface, or use a pasta machine. Use a sharp knife to cut fettuccine strips, powder them with rye flour so they don't stick, and simmer in salted water for 2-3 minutes, for al dente texture.
Drain water and add the pesto in the pan. Mix well to combine.
Distribute on serving plates, top with roasted tomatoes and a drizzle olive oil.
Serve right away.