Heat a large sauté pan over medium-low heat. Add the olive oil and heat through, then add the butter and allow it to melt.
Add the breadcrumbs, shaking the pan or stirring constantly until the breadcrumbs are uniformly golden brown, about 4 minutes. Immediately transfer from the pan to a bowl or container and store in an airtight container until ready to use, up to 5 days in advance.
For the tomato buttermilk:
Heat a small pot over medium heat, add the butter and allow to melt. Add the shallots and ¾ cup (177g) water and bring to a simmer. Simmer the onions, stirring occasionally until tender and water has mostly evaporated, about 20 minutes. Stir in the tomato paste and remove from heat and let cool.
Once cool, add the tomato shallot mixture and chilled buttermilk to a blender, food processor or use an immersion blender. Blend until smooth then season to taste with salt. Refrigerate until ready to use, at least 15 minutes and up to 2 days in advance.
For assembly:
Spoon ¼ cup (55g) of the tomato buttermilk dressing in the bottom of a large serving bowl or platter. Arrange the tomatoes over the top.
Drizzle with ⅓ cup (75g) of the tomato buttermilk dressing (reserving the remaining dressing for another use), drizzle with olive oil and season with salt and pepper. Finish with the buttered breadcrumbs and chives. Serve immediately.
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Notes
The tomato buttermilk can be made ahead of time and stored refrigerated in an airtight container for up to 5 days in advance.