Look for very small butternut squashes, or small to medium acorn squashes. If you find the hollow in a butternut isn't large enough, scoop a bit of the cooked flesh out before adding the egg.
Preheat oven to 425 degrees with racks in upper and lower thirds. Line 2 baking sheets with foil. Rub squashes all over with 1 tablespoon oil. Season with salt and thyme leaves, then place, cut-sides down, on a baking sheet. Add thyme sprigs. Place on upper rack; roast 10 minutes.
Meanwhile, toss tomatoes in remaining 1 tablespoon oil; season with salt. Spread on second sheet in a single layer. Place on lower rack; roast until tomatoes are beginning to collapse and squashes are tender, 20 to 25 minutes more.
Remove tomatoes. Turn squashes cut-sides up and roast 5 minutes more. If hollowsin squashes are large enough, spoon a tomato or two into each. Spoon 1/2 teaspoon chile paste into each hollow, then crack an egg into each; season with salt. Bake until whites are set but still a bit wobbly and yolks are soft, 12 to 15 minutes. (Start checking for donenessat early end of range, removing squashes with cooked eggs as they're done.) Let stand 3 minutes, then serve, with more chile paste and roasted tomatoes, and seasoned with pepper.