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1
Heat the oven to 375F.
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2
Mince the garlic cloves, thinly slice the white onion, and dice the carrot. Meanwhile, set a wide saucepan on the range, and turn the heat to medium. Add the oil, and when it's heated, add the garlic, and then the onion, and then the carrot. Cook until the garlic is fragrant, the onion is translucent, and the carrot is beginning to soften, about 10 minutes.
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3
Add the red wine to the pan. Let it bubble away until mostly dissolved, about 5 minutes. Then add the tomato paste. Stir to incorporate the vegetables into the paste, and then leave the pan alone for a few minutes. It's ok if the paste browns on the bottom a little.
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4
Now add the diced tomatoes, along with the rosemary, the thyme, the hot pepper paste, and the lemon zest. Let everything come together, and the tomato juices simmer down, 10 minutes.
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5
Meanwhile, rinse the can-goop of the beans, and then toss generously with salt and pepper. Add the beans to the tomato sauce, and then stir in 1/2 cup of the Parmesan, along with the pesto. Season to taste.
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6
Now crack each of the four eggs into the pan, spacing them so that they aren't touching too much. (This job is easier if you first make four indentations in the sauce with the back of a large spoon.) Top the eggs with the remaining Parmesan and a good crack of black pepper. Move the pan to the oven, and cook until the egg whites are set, about 15 minutes. (But start checking at 10 minutes, just to be sure.)
