You may be in luck, but you will be surprised

- some of the books show
In Lauder Churchyard there is a stone at the north stone: David Broomfield late factor to Earl of Lauderdale for 44yrs - Mar 1851 71 yrs
(burial see chirnside below)In Greenlaw MIs, etc:
Adam Broomfield
(1) 10 Jan 1826 84yrs, Elizabeth Purves his wife 16 Jul 1824 64yrs, Andrew Broomfield their son 5 Feb 1816 31yrs,, son Adam Broomfield
(2) 31 May 1835 35yrs and his wife Euphemia Phin 2 Jul 1853 49yrs. Isabella daughter of Adam Broomfield
(1)plaque on church: to memory of Thomas Broomfield a considerable benefactor to this parish and the publick buried here Aug 1667 by order of the Kirk Session of Greenlaw this is erected 1742 restored Kirk Session 1920
inscription on old church bell: "Thomas Brounfield his gift to the Kirk of Greenlaw 1696 and refounded 1726 R.M. fecit Edinburgh". he was farmer in Greenlawdean
In Chirnside MIs:
David Broomfield 8 Dec 1882 79yrs, wife Ceclia Burt 17 Jan 1870 57yrs, daughter Mary Ann 17 Jun 1867 28yrs, son David died at London 3 Dec 1900 55yrs, sons William David & George died in inf.
Grace Broomfield wife of Darling Postmaster Chirnside 13 Aug 1830 48yrs, children Robert 14 Feb 1829 9mths, Robert 30 Aug 1828 3yrs, Margaret 20 Jun 1834 19yrs, Susan 8 Oct 1834 13yrs, Helen 22 Nov 1839 30yrs, Barbara 19 Dec 1840 26yrs. Thomas Darling 3 Jan 1855 76yrs
David Broomfield, Lauder land steward and factor to the Right Honorable the Earl of Lauderdale for nearly 44 28 Mar 1851 71yrs, wife Susan Smith died at Lauder 1 Jan 1862 75yrs, son David Broomfield solicitor Kelso died there 24 Nov 1878 48yrs
David Roberts late gardener in Spences Mains 11 Oct 1749 50yrs, spouse Jean Hogarth 20 Sept 1775 61yrs, daughter Helen (wife of Thomas Broomfield) died 30 Oct 1821 77yrs
In Eccles MIs:
erected by Robert Smith, Leitholm son William 7 Oct 1819 21yrs, daughter Isabella 03 Jul 1822 11yrs, father 15 Nov 1821 81yrs, mother Catherine Broomfield 14 Feb 1822 75yrs. Robert Smith 21 Mar 1843 73yrs
John Smith, Leitholm daughter Betsy 27 Jan 1830 3yrs 6mths Mary Broomfield 13 Sept 1830 96th yr
In affectionate remembrance of James eldest of John Broomfield, Leitholm who died 20 Jul 1899 23yrs also the above John Broomfield who died 13 Mar 1910 61yrs also Sarah Burn his wife 15 May 1922 75yrs
A tribute of enduring affection by his wife to the well beloved John Fairbairn husband of Agnes Broomfield 1841-1897, also the above Agnes Broomfield died Leitholm 29 Jan 1913 72yrs
In loving memory pf my dear aunt Mary Broomfield wife of WC Robsob died 28 Oct 1933 83yrs
In Hutton MIs:
Alexander Broomfield 13 Feb 1759 25yrs, Thomas Broomfield, mason in Chirnside 7 Feb 1795 ?7yrs (poss 87 yrs), children: Jean, John & william died in Inf.
Janet Kerr wife of James Broomfield 13 Aug 1873 73yrs, grandson David Broomfield 11 May 1862 14yrs
Hope this helps - but best to checkout the whole of Berwickshire not just Lauder
ALSO
Try and get a copy of Lauder and Lauderdale by A Thomson first published 1902 republished 2001. it will surprise you

it explains the stone at Lauder more and mention the Broomfields (include David) as they where back when
there is a photopragh of quarter-master & honorary Captain Broomfield (Thomas)