Preheat the oven to 350°F (175°C). Lightly grease a rimmed baking sheet with olive oil.
Arrange the squash halves cut-side down on the baking sheet. Roast for about 45 minutes, or until a fork easily pierces the flesh. Larger squash may take longer.
Remove the squash and let it cool until you can handle it safely. Keep the oven on. Brush both sides of the bread slices lightly with olive oil and arrange them in a single layer on a baking sheet. Toast for 8 to 10 minutes, flipping halfway through with tongs, until golden and crisp.
While the bread toasts, heat the measured ½ tablespoon olive oil in a large skillet over medium heat. Add the shallots and cook, stirring, until tender and golden. Stir in the salt, using less initially if the nut butter is salted.
Scoop out the squash flesh and measure 1½ cups (360g). Save any extra for another dish and discard the skin. Add the measured flesh, cooked shallots and nut butter to a food processor.
Blend until smooth, stopping to scrape down the bowl as needed. Taste and adjust the salt.
Add the topping to the toasted bread slices and serve immediately.
